Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

Embed Size (px)

Citation preview

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    1/99

    Ca`vwtgx Scjgncg Dgvkxt`gnt

    Tgcmnjckl Xgvaxt

    NRW-CS-63-;9

    Nayg`hgx 84, 8663

    Tswnk`j? K Rkyglgt Taalejt iax Djstxjhwtgd Szstg`s

    Oksan K. Sejcgrjc Vgtgx K. Djndk

    Khstxkct

    Tmjs vkvgx dgscxjhgs tmg dgsjbn knd j`vlg`gntktjan ai Tswnk`j, k rkyglgt-hksgd

    ljhxkxz hwjlt ta gnca`vkss tmg xknbg ai xgsgkxcm ixa` aiiljng knklzsjs ai ca`vwtgx

    bgngxktgd xgsawxcg sjbnkls ta tmg canstxwctjan knd dgvlaz`gnt ai anljng szstg`s.

    Rkyglgt knklzsjs mks vxaygn ta hg kn jnyklwkhlg knklzsjs tgcmnj{wg iax djscaygxjnb

    cmkxkctgxjstjcs ai sjbnkls knd mks hggn kvvljgd ta `knz kxgks xglktgd ta ca`vwtgx

    szstg`s xgsgkxcm. Tswnk`j js cxgktgd `astlz iax wsg jn djstxjhwtgd szstg`s, da`kjnsrmgxg sgnsaxs kxg dgvlazgd ta sk`vlg xgsawxcg sjbnkls xglktgd ta masts knd ngtraxes,

    knd kxg wsgd iax `kejnb xwn-tj`g dgcjsjans jn kvvljcktjans. Ixa` tmg knklzsjs ai

    ca`vwtgx bgngxktgd xgsawxcg sjbnkls, anljng szstg`s `kz hg dgvlazgd wsjnb awx

    taalejt ta vxayjdg vgxiax`kncg bkjns jn wsgx kvvljcktjans. Rjtm Tswnk`j, k wsgx ckn

    sgk`lgsslz txknsjtjan ixa` sj`wlktjan ta dgvlaz`gnt ai k rkyglgt-hksgd anljng

    szstg`. Tmg taalejt dgsjbn js g}txg`glz bgngxkl jn tmkt tmg vxayjdgd jntgxikcgs ckn hg

    wsgd iax kl`ast knz tzvg ai kvvljcktjan tmkt `kz hgngijt ixa` rkyglgt kvvxakcmgs. Jt

    js klsa g}tgnsjhlg knd ilg}jhlg, kllarjnb wsgxs ta cwsta`jg tmgjx knklzsjs wsjnb tmg

    cakxsg- knd ijng-bxkjn hwjldjnb hlaces vxayjdgd jn tmg taalejt. Jn tmjs vkvgx, rg

    sw``kxjg tmg tgcmnj{wgs ai rkyglgt knklzsjs iax wsg jn ca`vwtgx szstg`s knd

    vxayjdg j`vlg`gntktjan dgtkjls ai tmg ljhxkxz ta vxayjdg k wsgx rjtm tmg vargx tarkyglgt-gnkhlg tmgjx kvvljcktjan. Rg dgscxjhg mar tmg taalejt ckn hg g}tgndgd, mar jt

    vgxiax`s jn tgx`s ai sk`vlg xktgs knd scklkhjljtz, knd mar jt ckn hg wsgd rjtm tmg

    XVS taalejt ta hwjld djstxjhwtgd rkyglgt szstg`s. Canclwsjans knd iwtwxg djxgctjans ai

    awx xgsgkxcm xglktgd ta tmjs taalejt rjll hg djscwssgd. Tswnk`j js kykjlkhlg ixa`

    mttv?!!rrr.cs.naxtmrgstgxn.gdw!~XVS.

    Giiaxt svansaxgd hz tmg Nktjankl Scjgncg Iawndktjan wndgx Bxknts KNJ66:388;, KCJ6;;8=:;, KNJ

    636;;6=, GJK6;36=9:, knd GJK688444:. Knz avjnjans, ijndjnbs knd canclwsjans ax

    xgca``gndktjans g}vxgssgd jn tmjs `ktgxjkl kxg tmasg ai tmg kwtmax knd da nat ngcgsskxjlz xgilgct tmg

    yjgrs ai tmg Nktjankl Scjgncg Iawndktjan -NSI*.

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    2/99

    Egzraxds? rkyglgt knklzsjs, sjbnkl vxacgssjnb, djstxjhwtgd szstg`s, xgsawxcg `anjtaxjnb

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    3/99

    Tswnk`j? K Rkyglgt Taalejt iax Djstxjhwtgd Szstg`s

    Oksan K. Sejcgrjc Vgtgx K. Djndk

    u osejt, vdjndkpFcs.naxtmrgstgxn.gdwDgvkxt`gnt ai Ca`vwtgx Scjgncg

    Naxtmrgstgxn Wnjygxsjtz

    Nayg`hgx 84, 8663

    Khstxkct

    Tmjs vkvgx dgscxjhgs tmg dgsjbn knd j`vlg`gntktjan ai Tswnk`j, k rkyglgthksgd ljhxkxz

    hwjlt ta gnca`vkss tmg xknbg ai xgsgkxcm ixa` aijng knklzsjs ai ca`vwtgx bgngxktgd xgsawxcg

    sjbnkls ta tmg canstxwctjan knd dgvlaz`gnt ai anljng szstg`s. Rkyglgt knklzsjs mks vxaygn

    ta hg kn jnyklwkhlg knklzsjs tgcmnj{wg iax djscaygxjnb cmkxkctgxjstjcs ai sjbnkls knd mks hggn

    kvvljgd ta `knz kxgks xglktgd ta ca`vwtgx szstg`s xgsgkxcm. Tswnk`j js cxgktgd `astlz iax wsg

    jn djstxjhwtgd szstg`s, k da`kjn rmgxg sgnsaxs kxg dgvlazgd ta sk`vlg xgsawxcg sjbnkls xglktgd

    ta masts knd ngtraxes, knd kxg wsgd iax `kejnb xwntj g dgcjsjans jn kvvljcktjans. Ixa`

    tmg knklzsjs ai tmgsg ca`vwtgx bgngxktgd xgsawxcg sjbnkls, anljng szstg`s `kz hg dgvlazgd

    wsjnb awx taalejt ta vxayjdg vgxiax`kncg bkjns jn wsgx kvvljcktjans. Rjtm Tswnk`j, k wsgx

    ckn sgk`lgsslz txknsjtjan ixa` sj`wlktjan ta dgvlaz`gnt ai k rkyglgthksgd anljng szstg`.

    Tmg taalejt dgsjbn js g}txg`glz bgngxkl jn tmkt tmg vxayjdgd jntgxikcgs ckn hg wsgd iax kl`ast

    knz tzvg ai kvvljcktjan tmkt `kz hggngt ixa` rkyglgt kvvxakcmgs. Jt js klsa g}tgnsjhlg kndg}jhlg, kllarjnb wsgxs ta cwsta`jg tmgjx knklzsjs wsjnb tmg cakxsg knd ngbxkjn hwjldjnb

    hlaces vxayjdgd jn tmg taalejt. Jn tmjs vkvgx, rg sw``kxjg tmg tgcmnj{wgs ai rkyglgt knklzsjs

    iax wsg jn ca`vwtgx szstg`s knd vxayjdg j`vlg`gntktjan dgtkjls ai tmg ljhxkxz ta vxayjdg k

    wsgx rjtm tmg vargx ta rkyglgtgnkhlg tmgjx kvvljcktjan. Rg dgscxjhg mar tmg taalejt ckn hg

    g}tgndgd, mar jt vgxiax`s jn tgx`s ai sk`vlg xktgs knd scklkhjljtz, knd mar jt ckn hg wsgd rjtm

    tmg XVS taalejt ta hwjld djstxjhwtgd rkyglgt szstg`s. Canclwsjans knd iwtwxg djxgctjans ai awx

    xgsgkxcm xglktgd ta tmjs taalejt rjll hg djscwssgd.

    Tswnk`j ckn hg darnlakdgd ixa` mttv?!!rrr.cs.naxtmrgstgxn.gdw!XVS.

    Giiaxt svansaxgd hz tmg Nktjankl Scjgncg Iawndktjan wndgx Bxknts KNJ66:388;, KCJ6;;8=:;, KNJ636;;6=, GJK

    6;36=9:, knd GJK688444:. Knz avjnjans, ndjnbs knd canclwsjans ax xgca``gndktjans g}vxgssgd jn tmjs `ktgxjkl

    kxg tmasg ai tmg kwtmax knd da nat ngcgsskxjlz xggct tmg yjgrs ai tmg Nktjankl Scjgncg Iawndktjan -NSI*.

    ;

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    4/99

    ; Jntxadwctjan

    Djstxjhwtgd szstg`s kxg hgca`jnb jncxgksjnblz kdkvtjyg, knd scmgdwljnb knd atmgx kdkvtktjan dgcj

    sjans kxg hgjnb `kdg kt kvvljcktjan, `jddlgrkxg, knd AS lgygls. Tmgsg dgcjsjans kxg `kdg kccaxd

    jnb ta tmg kykjlkhjljtz knd lakd ai `kcmjngs, knd klsa tmg ngtraxe candjtjans tmkt vxgykjl hgtrggn

    tmg `kcmjngs. Xgsawxcg `anjtaxjnb szstg`s vxayjdg tmjs jniax`ktjan, tzvjckllz jn tmg iax` aikvvxavxjktglz sk`vlgd ; vgxjadjc `gkswxg`gnts, ax djscxgtgtj`g xgsawxcg sjbnkls.

    Tmgxg kxg `knz wsgs ai xgsawxcg sjbnkls knd avgxktjans tmkn ckn hg kvvljgd ta tmg`, hwt tmg

    iallarjnb kxg, jn awx yjgr, `ast sjbnjckntlz j`vkctgd hz rkyglgt knklzsjs?

    Cmkxkctgxjktjan. Cmkxkctgxjjnb tmg dznk`jc hgmkyjax ai clkssgs ai sjbnkls vxayjdgs wsrjtm jnsjbmts jnta tmg hgmkyjax ai xgsawxcgs, tmgjx scmgdwlgxs, knd tmgjx mw`kn wsgxs.

    Sw``kxjktjan. Sw``kxjjnb ang ax k callgctjan ai sjbnkls `kegs jt gksjgx iax k mw`kn ax ksaitrkxg szstg` ta knsrgx {wgstjans.

    Djssg`jnktjan. Canygzjnb k xgsawxcg sjbnkl ax callgctjan ai xgsawxcg sjbnkls ixa` sgnsaxsta k callgctjan ai wsgxs smawld hg dang rjtm ks ljttlg ngtraxe txkic ks vassjhlg.

    Vxgdjctjan. Kdkvtjyg szstg`s ckxg khawt tmg iwtwxg hgmkyjax ai tmg xgsawxcg sjbnkl.

    Ta iwxtmgx awx -knd atmgxs* xgsgkxcm klanb tmgsg knd atmgx djxgctjans, rg mkyg dgyglavgd Tswnk`j,

    k rkyglgt taalejt iax wsg rjtm xgsawxcg sjbnkls jn djstxjhwtgd szstg`s. Tswnk`js dgsjbn js bgngxkl,

    knd g}tgntsjhlg, `kejnb jt wsgiwl jn atmgx da`kjns ks rgll.

    Rmz rkyglgt knklzsjs1 Rmjlg tmgxg kxg `knz knklzsjs tgcmjnj{wgs kvvljckhlg ta xgsawxcg sjb

    nkls, `ast mkyg djicwltjgs rmgn ikcgd rjtm nanstktjankxz ax nanvgxjadjc hgmkyjax. Rkyglgt

    tgcmnj{wgs aygxca`g tmgsg dgcjgncjgs, knd mkyg hggn smarn ta hg k vargxiwl knklzsjs taal iax

    wndgxstkndjnb sjbnkls jn bgngxkl knd, `axg svgcjckllz, ca`vwtgx xgsawxcg sjbnkls swcm ks mast

    lakd U8;P knd ngtraxe hkndrjdtm U;9P. K rkyglgt txknsiax` canygxts k vgxjadjckllz sk`vlgd, tj`gda`kjn sjbnkl jnta tra dj`gnsjans xgvxgsgntjnb tj`g knd scklg -ljeg ixg{wgncz*. Tmg awtvwts ai

    tmg rkyglgt txknsiax` kxg ckllgd tmg rkyglgt cagicjgnts, knd ckn hg stwdjgd jn ljgw ai tmg axjbj

    nkl sjbnkl iax tmgz cantkjn kll tmg jniax`ktjan jn jt. Aitgn k `axg g}jhlg knklzsjs ai tmg sjbnkl,

    ckllgd k `wltjxgsalwtjan knklzsjs -@XK*, js vxgigxxgd. Cmkxkctgxjktjan, sw``kxjktjan, djssg`j

    nktjan, knd vxgdjctjan jn rkyglgt da`kjn g}vasgs avvaxtwnjtjgs tmkt da nat g}jst jn tj`gda`kjn ax

    ixg{wgnczda`kjn. K rkyglgt da`kjn sjbnkl ckn hg xgkdjlz canygxtgd hkce ta tj`gda`kjn rjtmawt

    lass ai jniax`ktjan.

    Rmz Tswnk`j1 @knz j`vlg`gntktjans ai rkyglgt knklzsjs g}jst. Margygx, nang ai tmg` js

    twngd iax wsg jn xgsawxcg `anjtaxjnb jn k djstxjhwtgd szstg`, rmgxg rg xg{wjxg jng}vgnsjyg stxgk`

    jnb avgxktjan kt lar sk`vlg xktgs knd gicjgnt ca``wnjcktjan aygx lassz cmknngls. Jn kddjtjan,igr vxayjdg bgngxkljtz, kllarjnb tmg wsgx ta canstxwct gssgntjkllz kxhjtxkxz txknsiax`s jn vwxswjt ai

    xgsgkxcm bakls. Tmg Tswnk`j taalejt ckn hwjld kxhjtxkxz txknsiax s knd ckn kdkvtjyglz smkvg jts

    txknsiax`s kt xwntj`g. Nang tmkt rg mkyg iawnd, ckn hg xgkdjlz wsgd iax hatm aijng knd anljng

    knklzsjs. Jn kddjtjan, jt js djicwlt ta nd gicjgnt rkyglgt taals tmkt kxg nat owst hwjlt iax wsg an

    djbjtkl sjbnkl vxacgssaxs knd `knz taals tmkt rjll xwn an VCs kxg hwjlt iax aijng knklzsjs wsjnb

    ;Ta tmg hgst ai awx enarlgdbg, na ang mks stwdjgd tmg vxahlg` ai dgtgx`jnjnb kn kvvxavxjktg xktg ai sk`vljnb iax

    xgsawxcgs jn djstxjhwtgd ca`vwtjnb. Tmjs js jn awx iwtwxg vlkns.

    8

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    5/99

    scxjvtjnb lknbwkbgs knd kxg tmgxgiaxg nat gicjgnt iax wsg jn dgvlazjnb anljng szstg`s. Ijnkllz, tmg

    taalejts dgsjbn js avtj`jgd ta t njcglz jnta tmg XVS szstg` U7P iax ca``wnjcktjan, vxgdjctjan

    knd `anjtaxjnb.

    Tmg Tswnk`j taalejt js hwjlt wsjnb tmg C%% vxabxk``jnb lknbwknbg knd tmg Stkndkxd Tg`vlktg

    Ljhxkxz -STL* bgngxjc cantkjngx tzvgs. Tswnk`j ckn xwn rjtm `knz djiigxgnt jnvwt dktk tzvgs, knd

    ckn hg gksjlz g}tgndgd iax wsg jn szstg`s xgsgkxcm knd szstg` hwjldjnb.Tmg xg`kjndgx ai tmg vkvgx js ks iallars. Jn Sgctjan 8, rg hgbjn hz djscwssjnb xglktgd xgsgkxcm

    knd djiigxgntjktjnb Tswnk j ixa` atmgx rkyglgthksgd szstg s. Sgctjan 3 dgscxjhgs tmg dgcjgncjgs

    ai atmgx knklzsjs tgcmnj{wgs, knd dgtkjls tmg ktmg`ktjckl iawndktjans ai tmg rkyglgt txknsiax` knd

    tmg tmgaxz ai `wltjxgsalwtjan knklzsjs. Sgctjan 4 lkzs awt tmg bakls knd xg{wjxg`gnts ai Tswnk`j,

    raxejnb ixa` tmg vgxsvgctjyg ai k xgsgkxcmgx wsjnb awx szstg`.

    Ai vkxtjcwlkx jntgxgst ta k xgsgkxcmgx klxgkdz ik`jljkx rjtm rkyglgts, Sgctjan 7 dgscxjhgs mar

    ta bgt stkxtgd wsjnb Tswnk`j? darnlakdjnb, ca`vjljnb, wsjnb tmg ca``kndljng taals, knd rxjtjnb

    ngr taals. Sgctjan 9 cantjnwgs hz dgscxjhjnb tmg dgsjbn knd j`vlg`gntktjan ai tmg taalejt, rmjlg

    Sgctjan 2, dgscxjhgs kdykncgd wsgs ai Tswnk`j knd mar ta g}tgnd jt.

    Vgxiax`kncg js k cxjtjckl bakl jn k szstg` dgsjbngd iax wsg jn anljng gnyjxang`nts, swcm ksTswnk j. Jn Sgctjan =, rg `gkswxg tmg vgxiax`kncg ai tmg Tswnk`j taalejt jn tgx`s ai mar tmg

    szstg` scklgs knd vgxiax`s kt mjbm sk`vljnb xktgs. Rg klsa djscwss xgkltj g szstg` dglkzs, k

    vxavgxtz tmkt js iwndk`gntkl ta rkyglgt szstg`s hksgd an ckwskl ltgxs.

    Rg bgngxkllz wsg Tswnk`j klanb rjtm tmg Xgsawxcg Vxgdjctjan Szstg` -XVS* taalejt U7P. XVS

    vxayjdgs ca``wnjcktjan sgxyjcgs, vxgdjctjan sgxyjcgs, sgnsaxs, knd `knz atmgx taals. Sgctjan :

    dgtkjls tmg jntgxikcg ai Tswnk`j ta XVS. Wsjnb tmg jntgxikcg, rg mkyg hwjlt k nw`hgx ai XVS

    ca`vangnts tmkt jnclwdg rkyglgts. Wsjnb tmg ca`hjnktjan, rg mkyg g}vlaxgd wsjnb tmg vxgdjctjyg

    `adgls tmkt XVS aiigxs an tmg rkyglgt cagicjgnts ks kn kvvxakcm ta xgdwcjnb xgkltj`g szstg`

    dglkz. Rg mkyg klsa hwjlt k vxaaiaicancgvt xgsawxcg sjbnkl djssg jnktjan knd {wgxz szstg` jn

    rmjcm kvvljcktjans ckn swhscxjhg ta k stxgk` ai sk`vlgs kt k xktg knd xgsalwtjan tmkt js xjbmt iax

    tmgjx kvvljcktjan. Ijnkllz, jn Sgctjan ;6 rg vxayjdg canclwdjnb xg`kxes knd tmg xakd`kv ai awxiwtwxg raxe.

    8 Xglktgd raxe

    Rg kxg nat tmg xst ta sgg tmg wsgiwlngss ai wsjnb rkyglgthksgd tgcmnj{wgs iax stwdzjnb tmg hg

    mkyjax ai sjbnkls knd hwjldjnb anljng szstg`s. Xgsgkxcmgxs mkyg kvvljgd rkyglgthksgd tgcmnj{wgs

    ta wndgxstknd ngtraxe txkic knd vkcegt txkcgs iax sa`g tj`g. Tmg sglisj`jlkx nktwxg ai ngtraxe

    txkic rks kn j`vaxtknt djscaygxz jn tmg gkxlz :6s. Khxz, gt kl, mkyg dgyglavgd rkyglgthksgd

    tgcmnj{wgs ta gstj`ktg tmg Mwxst vkxk`gtgx, tmg dgbxgg ai sglisj`jlkxjtz U;P. Igld`knn, gt kl mkygg}tgnsjyglz wsgd rkyglgts ta cmkxkctgxjg ngtraxe txkic ks `wltjixkctkl U9P knd ta stwdz tmg j`

    vkct ai tmjs vxavgxtz an cantxal `gcmknjs`s swcm ks TCV canbgstjan cantxal U2P. Xjgdj, gt kl

    mkyg smarn mar ta wsg rkyglgts ta szntmgsjg ngtraxe txkic U;2P, ca`vwtjnb xgswlts jn kn gi

    cjgnt `knngx tmkt kvvgkx ta `ktcm xgkl Gtmgxngt txkcgs yjswkllz knd stktjstjckllz. [jka, gt kl mkyg

    g`vjxjckllz stwdjgd tmg vxgdjctkhjljtz ai rkyglgt cagicjgnts ai xgkl ngtraxe txkic iax wsg jn dg

    tgx`jnb `gsskbg txknsigx tj`gs U;9P. Sgygxkl rkyglgt szstg`s klsa g}jst. Iax g}k`vlg, RJND wsgs

    rkyglgthksgd sckljnb knklzsjs ta dgtgct ngtraxe vgxiax`kncg vxahlg`s U:P. Knatmgx xglgyknt szs

    3

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    6/99

    tg` gstj`ktgs tmg Mwxst vkxk`gtgx kt tmg xawtgx ta `keg kdkvtjyg cmknbgs jn canbgstjan cantxal, ax

    ta vxayjdg wv ta dktg jniax`ktjan khawt txkic dznk`jcs rjtmawt staxjnb kll ai tmg dktk iax aijng

    knklzsjs U;=P. Rg mkyg vxavasgd knatmgx anljng rkyglgt szstg` iax tmg djssg`jnktjan ai xgsawxcg

    jniax ktjan jn kn kccwxktg knd scklkhlg iksmjan ta kvvljcktjans ai ykxjaws bxknwlkxjtz U8;P, k bakl

    kcmjgygd tmxawbm wsg ai tmg Tswnk`j taalejt. Tmjs vxavaskl js djscwssgd iwxtmgx jn Sgctjan :.

    Jn tmjs xgvaxt, rg dgtkjl Tswnk`j, k rkyglgt ljhxkxz tmkt rg mkyg canstxwctgd ta mglv hgttgxwndgxstknd tmg dznk`jcs ai ca`vwtgx bgngxktgd xgsawxcg sjbnkls. Ixa` tmjs, rg mavg ta cxgktg

    knd dgvlaz djstxjhwtgd, anljng ca`vangnts iax kvvljcktjans tmkt ckn hgngt ixa` mkyjnb rkyglgt

    gnkhlgd kvvljcktjans iax wsg jn scmgdwljnb knd atmgx da`kjns. Tmg ljhxkxz mks hggn hwjlt ta sktjsiz

    `knz ai awx xgsgkxcm nggds tmkt mkyg nat hggn `gt glsgrmgxg. Tmgxg kxg `knz aijng rkyglgt knkl

    zsjs taals kykjlkhlg tmkt vxayjdg rkyglgt dgca`vasjtjans knd txknsiax`ktjans xglktgd ta rkyglgts.

    Taals tmkt rg mkyg wsgd jnclwdg tmg Rkyglgt Taalha} jn @ktlkh U84P knd tmg @ktlkh scxjvts cxg

    ktgd hz D. G. Ngrlknd jn mjs haae an svgctxkl knklzsjs U;7P. Margygx, `knz ai tmg bakls ai awx

    xgsgkxcm kxg ai k `axg dznk`jc, `axg kdkvtkhlg, knd bgngxkl nktwxg ngcgssjtktjnb tmg gnmkncgd

    iwnctjankljtz knd g}jhjljtz aygx g}jstjnb taals.

    Jn axdgx ta kddxgss bgngxkljtz, rg mkyg hwjlt tmg taal rjtm ngbxkjn hwjldjnb hlaces jn axdgxta cxgktg knz tzvg ai dgca`vasjtjan, nat lj`jtgd sj`vlz ta tmg stxwctwxg ai tmg rkyglgt txknsiax`

    knd rkyglgt vkcegts. Tmg taalejt js ca`vasgd ai ltgxs -IJX, JJX, gtc.*, cagicjgnts iax ltgxs,

    darnsk`vlgxs knd wvsk`vlgxs vkxk`gtgxjgd hz tmg xktg, knd stkbgs tmkt kbbxgbktg tmg ngbxkjn

    hlaces jnta trahknd stxwctwxgs. Ixa` tmg hwjldjnb hlaces, rg cxgktg `knz stkndkxd rkyglgt txkns

    iax`ktjans, knd mkyg jnclwdgd jntgxikcgs iax `wltjxgsalwtjan knklzsjs -@XK* iax ahtkjnjnb tmg

    kvvxa}j`ktjan knd dgtkjl sjbnkls. @XK rjll hg djscwssgd jn `axg dgtkjl jn Sgctjan 3. Jn kddj

    tjan, rg vxayjdg jntgxikcgs iax bgttjnb ca`hjnktjans ai tmgsg sjbnkls jnclwdjnb tmg rgll enarn

    txknsiax`, cansjstjnb ai ang cakxsg kvvxa}j`ktjan sjbnkl knd k sgt ai dgtkjl sjbnkls, knd knz atmgx

    vassjhlg `j} ai @XK sjbnkls. Tmjs kx`s tmg wsgxs ai awx taalejt rjtm tmg vargx ta laae kt `knz

    djiigxgnt tzvgs ai sjbnkls tmkt `kz hg wsgiwl ta tmgjx xgsgkxcm, nat lj`jtjnb tmg wsgx ta stkndkxd

    txknsiax`s. Tmjs mks vxaygn jnyklwkhlg jn awx stwdz ai tmg vxgdjctkhjljtz ai ngtraxe hkndrjdtm,rmgxg rg mkyg smarn tmkt hjnnjnb knd @XK knklzsjs an kvvxa}j`ktjan sjbnkls kxg sj`jlkx U;9P.

    @knz ai tmg g}jstjnb aijng taals kxg nat ks xwntj`g ixjgndlz ks rg tmjne ngcgsskxz ta kdkvt

    ta {wjce cmknbjnb xgsawxcg sjbnkls. Jn tmg Tswnk j taalejt, rg vxayjdg jntgxikcgs ta dznk`jckllz

    kdkvt tmg txknsiax` knd tmg dgca`vasjtjan ta tmg cmkxkctgxjstjcs ai tmg jnvwt xgsawxcg sjbnkl. Rg

    nd tmkt tmg stktjc txknsiax`ktjans tmkt kxg tzvjckllz iawnd jn aijng taalha}gs kxg jnswicjgnt ta

    vxavgxlz stwdz mar ta kdkvt tmg knklzsjs ta tmg cmknbgs jn k bjygn jnvwt sjbnkl. Rg gnyjsjan k

    wsgx ai tmg taalha} dznk`jckllz kddjnb ax xg`ayjnb lgygls jn tmg dgca`vasjtjan hksgd an gvacm

    cmknbgs dgtgctgd jn tmg xgsawxcg sjbnkl. Kt tmjs tj`g, tmg taalha} dags nat cantkjn `gcmknjs s

    iax dgtgctjnb gvacm cmknbgs, hwt js sa`gtmjnb tmkt rg vlkn ta laae jnta jn awx iwtwxg xgsgkxcm. Jn

    kddjtjan ta dznk`jc stxwctwxkl cmknbgs, tmg taalejt kllars iax dznk`jckllz cmknbjnb tmg rkyglgthksjs iwnctjans kt xwntj`g. Tmjs ckn lgssgn ca`vwtktjankl ca`vlg}jtz ai tmg szstg` rmgn k largx

    axdgx hksjs iwnctjan ckn vxayjdg ks `wcm hgngt ks k mjbmgx axdgx ang. Tmjs tzvjckllz accwxs rmgn

    k vkxtjcwlkx ixg{wgncz hknd mks lar gngxbz knd tmgxgiaxg tmg ltgxjnb ai tmjs hknd js nat smarjnb

    knztmjnb jntgxgstjnb. Tmg jdgk ai tj`gykxzjnb avgxktjan, kdkvtjnb vkxk`gtgxs ai tmg txknsiax` ta

    tmg sjbnkl cmkxkctgxjstjcs kt xwntj`g, js k ygxz kvvgkljnb kxgk ai xgsgkxcm tmkt rg mavg `kz lgkd

    ta vgxiax`kncg bkjns jn vxgdjctjan knd scmgdwljnb jn djstxjhwtgd szstg`s. @knz ai tmg dznk`jc

    jntgxikcgs tmkt mkyg hggn cxgktgd jn Tswnk`j js jniax`gd hz tmg raxe ai Sadkbkx gt kl U83P.

    4

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    7/99

    Tmg Tswnk`j ljhxkxz ckn klsa hg wsgd ta hwjld anljng, rkyglgtgnkhlgd szstg`s. Ang kvvlj

    cktjan tmkt rg mkyg tmawbmt khawt jn dgtkjl js jn xgsawxcg djssg`jnktjan knd xgsawxcg vxgdjctjan

    jn djstxjhwtgd kvvljcktjans. Margygx, tmg ljhxkxz ckn hg wsgd iax hwjldjnb atmgx tzvgs ai anljng

    szstg`s ks rgll. Kn g}txg`glz vargxiwl hgngt ai tmg taalejt, js tmkt tmg txknsjtjan ixa` knklz

    sjs!sj wlktjan, ta hwjldjnb anljng szstg`s js yjxtwkllz giiaxtlgss. Tmg ljhxkxz ckn hg wsgd jn gjtmgx

    `jndsgt xjbmt awt ai tmg ha}. Tmjs js k vargxiwl kdykntkbg aygx @ktlkh gygn tmawbm @ktlkh cantkjns wtjljtjgs iax ca`vjljnb `lg scxjvts jnta g}gcwtkhlgs.

    Kddjtjankllz, ji k wsgx rknts ta wsg Tswnk`j jn canownctjan rjtm tmg Xgsawxcg Vxgdjctjan Szs

    tg` -XVS*, tmg Tswnk`j taalejt rjll hg jnclwdgd rjtm tmg ng}t XVS ygxsjan xglgksg. Tmg XVS

    xglgksg cadg cantkjns jntgxikcg clkssgs hgtrggn Tswnk`j knd XVS sa tmkt xgsgkxcmgxs ckn g}tgnd

    cwxxgnt kvvljcktjans ta wsg rkyglgts rjtm tj`gsgxjgs knklzsjs knd XVS ca``wnjcktjan canstxwcts.

    3 Rkyglgt djscwssjan

    Jn axdgx ta `atjyktg tmg xgksans iax rmz rkyglgts kxg k vargxiwl taal iax sjbnkl knklzsjs, jt jsjniax`ktjyg ta mjbmljbmt tmg dgcjgncjgs ai atmgx knklzsjs tgcmnj{wgs. Tmg Ikst Iawxjgx Txknsiax`

    -IIT*, k tgcmnj{wg wsgd iax knklzjnb tmg ixg{wgncz cantgnt ai k sjbnkl, anlz vxayjdgs ixg{wgncz

    jniax`ktjan, smarjnb natmjnb khawt mar k sjbnkl cmknbgs jn tj`g. Dwg ta tmjs lj`jtktjan, tmg tj`g

    da`kjn xgvxgsgntktjan cknnat hg g}kctlz xgcanstxwctgd ixa` tmg IIT awtvwt wnlgss tmg jnvwt js

    vgxjadjc jn tj`g. Tmg Smaxttgx Iawxjgx Txknsiax` -STIT* kttg`vts ta salyg tmjs lj`jtktjan hz

    knklzjnb sjbnkl cmknbgs jn hatm tj`g knd jn ixg{wgncz. Tmg STIT vgxiax`s kn IIT aygx k }gd

    sjg rjndar tmkt sljdgs aygx tj`g. Tmg tj`g dznk`jcs kxg ckvtwxgd hz yjgrjnb tmg sjbnkl jn k }gd

    sjg rjndar, knd tmg ixg{wgncz hz tmg ca`vwtktjan ai tmg IIT aygx tmkt rjndar. Tmjs tgcmnj{wg

    vxayjdgs kn gstj`ktg ai mar tmg sjbnkl cmknbgs jn hatm tj`g knd ixg{wgncz, hwt js lj`jtgd hz tmg

    rjndar sjg. Ji tmg rjndar sjg js `kdg s`kll, tmg knklzsjs vxayjdgs ngbxkjn tj`g xgsalwtjan knd

    cakxsgbxkjn ixg{wgncz xgsalwtjan. Ks tmg rjndar sjg jncxgksgs, tmg canygxsg js txwg. Tmgxgiaxg jtjs skjd tmkt tmg STIT swiigxs ixa` tmg Mgjsgnhgxb Wncgxtkjntz Vxjncjvlg hgtrggn g}kct enarlgdbg

    ai gjtmgx tj`g ax ixg{wgncz. Tmg rkyglgt knklzsjs aygxca`gs hatm lj`jtktjans ai tmg IIT knd tmg

    STIT, knd js tmgxgiaxg kn g}txg`glz wsgiwl tgcmnj{wg iax knklzjnb sjbnkls tmkt cmknbg xkvjdlz jn

    hatm tj`g knd ixg{wgncz, k cmkxkctgxjstjc tmkt ca`vwtgx bgngxktgd sjbnkls tgnd ta g}mjhjt.

    Jn Ijbwxg ;, rg dgscxjhg tmg bgngxkl sz`hals wsgd jn tmjs sgctjan ta dgscxjhg tmg sjbnkl vxa

    cgssjnb ksvgcts ai rkyglgt knklzsjs. Jn Ijbwxg 8, rg dgscxjhg sz`hals svgcjc ta tmg @XK rkyglgt

    knklzsjs.

    Jn rmkt iallars, rg vxayjdg kn aygxyjgr ai rkyglgts ks k taal iax knklzsjs, knd rmkt jt `gkns

    ta vxayjdg k `wltjxgsalwtjan yjgr ai k sjbnkl. Jn awx raxe, rg tkeg angdj`gnsjankl xgsawxcg

    sjbnkls, vgxjadjckllz sk`vlgd, knd txksiax` tmg` jnta tradj`gnsjans, xgvxgsgntjnb tj`g knd scklg-ljeg ixg{wgncz*. Tmg sjbnkl js dgca`vasgd jnta k nw`hgx ai lgygls xgvxgsgntjnb nat anlz hknds ai

    ixg{wgncz jniax`ktjan, hwt klsa tmg tj`g dznk`jcs tmkt accwx jn gkcm ixg{wgncz hknd. Tmg rkyglgt

    tgcmnj{wg js tmg swvgxjax `gtmad ta yjgr mar k sjbnkl cmknbgs jn k ixg{wgncz hknd kt k vkxtjcwlkx

    tj`g, knd js skjd ta g}mjhjt baad tj`gixg{wgncz lackljtz.

    Ks kn g}k`vlg ai k rkyglgt dgca`vasjtjan, jn Ijbwxg 3 -k*, rg smar k txkcg ai tmg lakd an

    k mast `kcmjng svknnjnb =;:8 sgcands -kvvxa}j`ktglz 8 ;!8 mawxs* sk`vlgd kt k ;M xktg. Tmgmast lakd sjbnkl js tmgn jnvwt jnta k rkyglgt txknsiax` hlace, tmws dgca`vasjnb tmg sjbnkl jnta

    7

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    8/99

    Sz`hal Dgscxjvtjan

    Bgngxkl sjbnkl vxacgssjnb

    T Jntgxykl ai tj`g hgtrggn swhsg{wgnt sk`vlgs.n Xgvxgsgnts tmg smaxt iax` ainT, hwt sjncg tmg sjbnkls tmkt rg

    gncawntgx jn awx raxe kxg vgxjadjckllz sk`vlgd, T js j`vljgd.

    i Ixg{wgncz jn M knd i 0 ;!T.is Tmg sk`vljnb ixg{wgncz jn M knd is 0 ;!T. Knbwlkx ixg{wgncz jn xkdjkns!sgc knd 0 8is Tmg sk`vljnb knbwlkx ixg{wgncz jn xkdjkns!sgc knd s 0 8is.}-n* ax }n Jnvwt xgsawxcg sjbnkl jndg}gd hz n.@ Tmg nw`hgx ai trahknd ltgx hknes wsgd ta dgca`vasg k sjbnkl. Jt js

    klsa tmg nw`hgx ai jndjyjdwkl kvvxa}j`ktjan knd dgtkjl sjbnkls kykjlkhlg.

    bk-n* Tmg ltgx cagicjgnts ai tmg larvkss knklzsjs ltgx.Bk-* Tmg _txknsiax` ai tmg larvkss knklzsjs ltgx -ixg{wgncz xgsvansg*.mk-n* Tmg ltgx cagicjgnts ai tmg mjbmvkss knklzsjs ltgx.Mk-* Tmg _txknsiax` ai tmg mjbmvkss knklzsjs ltgx -ixg{wgncz xgsvansg*.zj-n* Swhhknd sjbnkls tmkt kxg awtvwt ixa` tmg vxacgss ai ltgxjnb knd darn

    sk`vljnb.

    bs-n* Tmg ltgx cagicjgnts ai tmg larvkss szntmgsjs ltgx.Bs-* Tmg _txknsiax` ai tmg larvkss szntmgsjs ltgx -ixg{wgncz xgsvansg*.ms-n* Tmg ltgx cagicjgnts ai mjbmvkss szntmgsjs ltgx.Ms-* Tmg _txknsiax` ai tmg mjbmvkss szntmgsjs ltgx -ixg{wgncz xgsvansg*.c K canstknt sckljnb ikctax ta ca`vkxg }n rjtm }n.}-n* ax }n Tmg xgcanstxwctgd sjbnkl ixa` tmg swhhknd sjbnkls zj-n*.nd Jntgbgxyklwgd szstg` dglkz. Yklwg ai dglkz js dgvgndgnt an stxwctwxg knd

    ltgx axdgx.

    Ijbwxg ;? Tkhlg ai bgngxkl sjbnkl vxacgssjnb sz`hals wsgd ta dgscxjhg tmg `ktmg`ktjckl iawndktjan

    ai rkyglgt knklzsjs.

    ;4 lgygls zjgldjnb tmg rkyglgt cagicjgnts. Jn -h*, tmg s{wkxgd rkyglgt cagicjgnts kxg smarn jntmxgg dj`gnsjanjans. Tmg hxjbmtngss ai gkcm hlace tmgn caxxgsvands ta tmg gngxbz ai gkcm rkyglgt

    cagicjgnt. Tmg zk}js caxxgsvands ta tmg scklg ai tmg txknsiax , knd tmg }k}js caxxgsvands ta

    tj`g. Vggxjnb jnta tmjs vjctwxg {wklktktjyglz, tmg j`vwlsgs jn tj`g tmkt xgvxgsgnt k smkxv jncxgksg jn

    szstg` lakd kxg sggn. Ks kn g}k`vlg, tmg j`vwlsg tmkt accwxs kxawnd sk`vlg 4666 jn -k* js smarnkt `knz scklgs jn tmg gngxbz vlat ai tmg rkyglgt cagicjgnts. Gkcm lgygl ckvtwxgs tmg sk`g k`awnt

    ai tj`g, hwt gkcm lgygl mks igrgx cagicjgnts hz k ikctax ai tra. Ta `keg tmjs vajnt `axg cancxgtg,jn Ijbwxg 4 rg smar hz lgygl nw`hgx tmg vgxjad hgtrggn cagicjgnts -T*, tmg nw`hgx ai sk`vlgsjn gkcm scklg, knd tmg ixg{wgncz cantgnt tmkt js ckvtwxgd jn gkcm hknd ji rg kssw`g tmkt tmg jnvwt

    sjbnkl js hkndlj`jtgd ta k ixg{wgncz aiis!8. Tmjs bwxg js djxgctlz `ktcmgd ta tmg jniax`ktjan jnIjbwxg 3.

    Ks rg lgkxn `axg khawt rkyglgts, tmg jniax`ktjan dgscxjhgd jn tmg vxgyjaws vkxkbxkvm rjll

    hgca`g `axg clgkx. Ng}t rg dgscxjhg tmg hksjc hwjldjnb hlaces ai k rkyglgt knklzsjs.

    9

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    9/99

    Sz`hal Dgscxjvtjan

    @wltjxgsalwtjan knklzsjs

    kvvxa}o Tmg otm kvvxa}j`ktjan sjbnkl jn tmg dgca`vasjtjan.

    dgtkjlo Tmg otm dgtkjl sjbnkl jn tmg dgca`vasjtjan.

    o Swhsvkcg jndjcg tmkt xknbgs ixa` 6, . . . ,@ , knd xgvxgsgnts rmjcm scklg.

    n Sk`vlg jndjcg tmkt xknbgs ixa` 6, . . . , 8o

    knd xgvxgsgnts rmjcm cagicjgnt.6 Tmg `atmgx rkyglgt iwnctjan.6 Tmg sckljnb iwnctjan.o,n Tmg hkndvkss rkyglgt iwnctjan kt scklg o, cagicjgnt n.o,n Tmg larvkss sckljnb iwnctjan kt scklg o, cagicjgnt n.t Xgvxgsgnts tj`g jn sgcands.uYop K callgctjan ai ngstgd swhsvkcgs.k}-o,n* Tmg kvvxa}j`ktjan cagicjgnts vxadwcgd ixa` jnvwt sjbnkl } kt scklg o knd

    cagicjgnt n.d}-o,n* Tmg dgtkjl cagicjgnts vxadwcgd ixa` jnvwt sjbnkl } kt scklg o knd

    cagicjgnt n.Vxao]Z Tmg vxaogctjan ai sjbnkl ] jnta swhsvkcg Z.

    Ijbwxg 8? Tkhlg ai `wltjxgsalwtjan knklzsjs sz`hals wsgd ta dgscxjhg tmg `ktmg`ktjckl iawndktjan

    ai rkyglgt knklzsjs.

    3.; Tmg hksjc hwjldjnb hlaces knd stxwctwxgs

    Ta stkxt awx djscwssjan, rg rjll dgtkjl tmg hwjldjnb hlaces ai tmg rkyglgt txknsiax`, tmg tracmknngl

    djbjtkl ltgx hkne smarn jn Ijbwxg 7. Ixa` tmjs, kll atmgx xgvxgsgntktjans ixa` wnjiax` ltgx hknes

    ta nanwnjiax` ltgx hknes knd tmg rkyglgt dgca`vasjtjan iallar nktwxkllz. Jn tmg `ast sj`vlg

    cksg, kn jnvwt xgsawxcg sjbnkl, }-n*, k hkndlj`jtgd sjbnkl rjtm tzvjckl jnvwt svgctxw` smarn jn -k*,

    vgxjadjckllz sk`vlgd kt k xktg ais 0 8, js dgca`vasgd jnta tra hknds wsjnb djbjtkl ltgxs. Kssmarn jn -h*, }-n* js jnvwt jnta tmg ltgxs Bk-*, k lar vkss ltgx, knd Mk-*, k mjbm vkss ltgx. Tmg`kbnjtwdg xgsvansg ai tmgsg tra ltgxs kxg smarn jn -c*. Tmg vwxvasg ai tmgsg tra ltgxs js ta svljt

    tmg wndgxlzjnb xgsawxcg sjbnkl jnta tra mkli hknd sjbnkls xgvxgsgntjnb tmg mjbm knd lar ixg{wgncz

    jniax`ktjan. Sjncg tmg lar knd mjbm ixg{wgncz jniax`ktjan nar anlz cantkjn mkli tmg jniax`ktjan

    ks hgiaxg tmg avgxktjan, gkcm awtvwt ckn hg xgsk`vlgd darn hz k ikctax ai tra rjtmawt lass ai

    jniax ktjan. Tmg avgxktjan ai xgsk`vljnb darn hz k ikctax ai tra js enarn ks dgcj`ktjan. Tmg

    awtvwts ai tmg ltgx kxg tzvjckllz ckllgd tmg swhhknd sjbnkls. Tmgsg sjbnkls, dgsjbnktgd hz z6-n*knd z;-n*, kxg xgsk`vlgd ta mkli tmg axjbjnkl sk`vlg xktg, knd xgvxgsgnt tra axtmabankl sljcgs aiixg{wgncz jn tmg jnvwt xgsawxcg sjbnkl.

    Tmg swhhknd sjbnkls ckn hg `knjvwlktgd jn sa`g rkz hksgd an tmg kvvljcktjan. Iax g}k`vlg,k ca`vxgssjan kvvljcktjan `jbmt laae iax tmg hknd rjtm lgss tankl jniax`ktjan, knd xgdwcg tmg

    k`awnt ai jniax`ktjan jn tmjs hknd kvvxavxjktglz. Ancg kn kvvljcktjan dags tmg kvvxavxjktg `k

    njvwlktjan ai tmg swhhknd sjbnkls, jt js tmgn kvvxavxjktg ta g}vknd tmg sjbnkl hz tra ta ahtkjn tmg

    axjbjnkl sk`vljnb xktg, knd tmgn xgcanstxwct tmg xgsawxcg sjbnkl wsjnb tmg szntmgsjs ltgxs Bs-*knd Ms-*. Ji tmg knklzsjs knd szntmgsjs ltgxs kxg dgsjbngd kccaxdjnblz, tmg xgcanstxwctgd sjbnkl,}-n*, ckn hg g}kctlz tmg jnvwt sjbnkl ngblgctjnb {wkntjktjan najsg knd dglkz dwg ta ckwskl ltgxs.Tmg szstg` js skjd ta mkyg tmg vgxigct xgcanstxwctjan -VX* vxavgxtz ji}-n* 0 c }-n nd* iax

    2

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    10/99

    6 8666 4666 9666 =666 ;66666

    6.8

    6.4

    6.9

    6.=

    ;

    ;.8

    ;.4

    ;.9

    ;.=

    La

    kd

    n

    -k*

    Lgygl

    Rkyglgt cagiijcjgnts766 ;666 ;766 8666 8766 3666 3766 4666

    ;

    3

    7

    2

    :

    ;;

    ;3

    -h*

    Ijbwxg 3? G}k`vlg rkyglgt dgca`vasjtjan iax xgsawxcg sjbnkl mast lakd? -k* mast lakd txkcg iax

    =;:8 sgcands, -h* `gkn s{wkxg gngxbz ai tmg rkyglgt cagicjgnts -hlkce jndjcktgs lar gngxbz, ljbmt

    jndjcktgs mjbmgx gngxbz*.

    sa`g c 0 6 knd sa`g jntgbgx nd U87P. @wcm raxe mks bang jnta dgsjbnjnb tmg vxavgxtjgs ai vgxigct xgcanstxwctjan iax stxwctwxgs ai tmjs tzvg. @ast natkhlz js tmg `gtmad enarn ks tmg canowbktg

    {wkdxktwxg ltgx -C[I* `gtmad hz S`jtm knd Hkxnrgll jn ;:=4 knd lktgx vwhljsmgd ks k oawxnkl

    kxtjclg jn ;:=9 U88P. Rg wsg tmg C[I `gtmad jn tmg Tswnk`j taalejt ta dgxjyg ixa` tmg ltgx Bk-*,tmg cagicjgnts iax tmg atmgx tmxgg ltgxs, Mk-*, Bs-* knd Ms-*.

    Ixa` tmg bgngxkl stxwctwxg ai tmg trahknd ltgx hkne, `knz atmgx sjbnkl dgca`vasjtjans cknhg canstxwctgd. Tmg `ast natkhlg dgca`vasjtjan xgvxgsgntgd jn awx taalejt js tmkt ai tmg txgg

    stxwctwxgd rkyglgt dgca`vasjtjan. Tmjs js smarn jn Ijbwxg 9. Jn -k*, tmg stxwctwxg js smarn ks

    k txgg rmasg nadgs bxar jn ang djxgctjan, rmgxg tmg largst ixg{wgncz ca`vangnt ai tmg tra

    hknd svljt js jnvwt jnta knatmgx trahknd ltgx hkne. Tmjs cantjnwgs wv tmg txgg wntjl tmg sjbnkl

    mks hggn dgca`vasgd jnta tmg vxavgx nw`hgx ai hknds, dgsjbnktgd hz @% ;. Jn `knz szstg`s,tmg `wltjscklg xgvxgsgntktjan js `knjvwlktgd jn sa`g clgygx rkz ax sgnt aygx tmg ngtraxe ta hg

    xgcanstxwctgd hz ykxjaws djstxjhwtgd kvvljcktjans. Tmg xgcanstxwctjan vkxt ai tmg stxwctwxg mks tmg

    =

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    11/99

    Dgca`vasjtjan Vgxjad Nw`hgx ai Ixg{wgncz Ixg{wgncz

    lgygl jn sgcands vajnts lar mjbm

    Jnvwt 0 ;M ; n 6 is!86 8 n!8 is!4 is!8; 4 n!4 is!= is!48 = n!= i

    s!;9 i

    s!=

    3 ;9 n!;9 is!38 is!;94 38 n!38 is!94 is!387 94 n!94 is!;8= is!949 ;8= n!;8= is!879 is!;8=2 879 n!879 is!7;8 is!879= 7;8 n!7;8 is!;684 is!7;8: ;684 n!;684 is!864= is!;684

    ;6 864= n!864= is!46:9 is!864=;; 46:9 n!46:9 is!=;:8 is!46:9;8 =;:8 n!=;:8 is!;93=4 is!=;:8;3 =;:8 n!=;:8 6 is!;93=4

    Ijbwxg 4? Iallarjnb tmg djkbxk` ai Ijbwxg 3 -h*, rg smar tmg dgca`vasjtjan lgygl, tmg vgxjad

    -T*, tmg nw`hgx ai vajnts kt gkcm lgygl -n 0 nw`hgx ai vajnts kt ;M xktg* knd tmg ixg{wgnczxknbg jniax`ktjan kt gkcm lgygl jn tmg dgca`vasjtjan.

    xgygxsg txgg rjtm vkjxs ai szntmgsjs ltgx hknes `ktcmgd wv rjtm tmg ykxjaws lgygls ai tmg knklzsjs

    ltgx hknes. Tmjs txgg stxwctwxgd ltgx hkne mks k nanwnjiax` dgca`vasjtjan ai tmg jnvwt xgsawxcg

    sjbnkl knd js smarn -nat g}kctlz ta scklg* jn -h*. Kn g{wjyklgnt stxwctwxg ta tmkt xgvxgsgntgd jn-k* js smarn jn Ijbwxg 2 -k*. Jn tmjs bwxg kll tmg ykxjaws ltgxs ai tmg txgg mkyg hggn canyalygd

    jnta k sjnblg ltgx iallargd hz k sjnblg darn sk`vljnb ca`vangnt ai tmg kvvxavxjktg xktg. Sjncg

    tmg avgxktjan js dzkdjc, nanwnjiax`, knd labkxjtm`jckllz dgca`vasgd, tmg darnsk`vljnb xktgs

    jncxgksg ixa` hatta` ta tav hz vargxs ai tra. Jn -h*, tmg bgngxkl stxwctwxg ai ltgx hknes kxg

    smarn, xgvxgsgntjnb hatm nanwnjiax` knd wnjiax` dgca`vasjtjans. Jn k wnjiax` dgca`vasjtjan,

    gkcm ai tmg xj kxg g{wjyklgnt ta tmg nw`hgx ai hknds jn tmg dgca`vasjtjan. Iax g}k`vlg, ji rg wsgk ;6 lgygl dgca`vasjtjan, xj 0 ;6 iax kll j.

    Tmgxg kxg nw`gxaws txkdgaiis hgtrggn tmg stxwctwxgs, knd tmg tzvgs ai ltgxs tmkt kxg wsgd jn

    tmg knklzsjs knd szntmgsjs stkbgs. K `koax txkdgaii js tmg szstg` dglkz hgtrggn tmg jnvwt xgsawxcgsjbnkl, }-n*, knd tmg xgcanstxwctgd szstg` awtvwt, c }-nnd*. Hgckwsg jn kll cksgs jt js hgngcjklta `jnj`jg tmg xgkltj`g szstg` dglkz, tmg tzvg ai stxwctwxg knd tmg axdgx ai ltgx cagicjgnts

    `wst hg cmasgn ckxgiwllz. Lktgx jn tmjs xgvaxt, Sgctjan =, rg vxayjdg kn knklztjckl knklzsjs ai

    tmg xgkltj`g szstg` dglkz hksgd an tmg nanwnjiax` stxwctwxg, tmg avgxktjan tzvg knd tmg axdgx

    ai tmg ltgx cagicjgnts. Xgkltj`g szstg` dglkz js kn j`vaxtknt jsswg tmkt `wst hg kddxgssgd ta

    xgkljg jntgxkctjyg, rkyglgthksgd djstxjhwtgd szstg` kvvljcktjan hwjldjnb. Jt js kn j`vaxtknt dgsjbn

    cansjdgxktjan tmkt js tzvjckllz hksgd an tmg dglkz sjbnktwxg ai tmg kvvljcktjan.

    :

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    12/99

    6

    *- org]

    -k*

    Bk-*

    Mk-* Ms-*

    Bs-*

    8

    8

    8

    8

    %

    }-n*}-n*^

    Knklzsjs ijltgxs Dgcj ktaxs G}vkndgxs Szntmgsjs ijltgxs

    Xgcanstxwctgd

    sjbnkl

    Jnvwt

    sjbnkl

    z6-n*

    z;-n*

    Swhhknd

    sjbnkls

    -h*

    8

    6

    *- ork gM

    *- ork gB

    -c*

    Ijbwxg 7? Sj`vlg djscwssjan ai rkyglgts? -k* tzvjckl svgctxw` ai xgsawxcg sjbnkl, -h* tmg tra

    cmknngl djbjtkl ltgx hkne, -c* tzvjckl ltgx xgsvansgs ai trahknd ltgx hkne.

    3.8 @wltj-xgsalwtjan knklzsjs

    Jt js j`vaxtknt ta dgscxjhg ta tmg xgkdgx rmkt js `gknt hz k rkyglgthksgd `wltjxgsalwtjan knklzsjs.

    Ijbwxg = smars tmjs {wkljtktjyglz. Tmg bwxg smars kn jnvwt sjbnkl }n, xgvxgsgntjnb kn kvvxavxjktglz sk`vlgd, ngbxkjn xgsawxcg sjbnkl, tmg hjnnjnb ai k ngtraxe hkndrjdtm txkcg. Tmg jnvwt

    sjbnkl js hgjnb dgca`vasgd jnta tmxgg xgsalwtjan stkbgs ca`vasgd ai kvvxa}j`ktjan knd dgtkjl

    sjbnkls. Hz txkygxsjnb tmg kvvxa}j ktjan txgg -kvvxa}o , o jncxgksjnb*, rg ahsgxyg tmkt gkcm aitmg vlats nat anlz mkyg igrgx vajnts, hwt dgscxjhg k cakxsgx kvvxa}j`ktjan ai tmg wndgxlzjnb jnvwt

    sjbnkl. Gkcm swccgssjyg kvvxa}j`ktjan cantkjns mkli tmg nw`hgx ai vajnts knd ckvtwxgs mkli ai tmg

    ixg{wgncz cantgnt ai tmg vxgyjaws kvvxa}j`ktjan. Gygn tmawbm ks o jncxgksgs gkcm kvvxa}j`ktjanmks igrgx vajnts, gkcm bxkvm js stjll caygxjnb tmg sk`g vgxjad ai tj`g. Hz ahsgxyjnb tmg dgtkjls,rg ckn {wkljtktjyglz sgg tmkt tmg k`awnt ai jniax`ktjan tkegn krkz ixa` gkcm kvvxa}j`ktjan kt

    swhsg{wgnt lgygls js tmg dgtkjl. Tmkt js, kvvxa}o 0 kvvxa}o; dgtkjlo . Tmg ltgxs knd kxgdgxjygd ixa` tmg rkyglgt hksjs iwnctjan.

    Tmg iallarjnb djscwssjan js jniax`gd hz tmg raxe ai @kllkt U;8P, Dkwhgcmjgs U4P, knd Khxz, gt

    kl U8P. Tmg stxwctwxg smarn jn tmg bwxg js tmg djscxgtg rkyglgt txknsiax` -DRT*, k `ktmg`ktjckl

    txknsiax`ktjan iax xgvxgsgntjnb k ;dj gnsjankl djscxgtg tj`g sjbnkl}n. Jntwjtjyglz, tmg DRT svljts

    ;6

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    13/99

    ]n

    Lgygl 6

    Lgygl;

    Lgygl @8

    Lgygl @;

    Lgygl @

    Lgygl @%;

    Ngtraxe

    SgnsaxKvv

    ]n^

    8LVI

    MVI 8

    8LVI

    MVI 8

    8LVI

    MVI 8

    8LVI

    MVI 8

    8LVI

    MVI 8

    Lgygl @%;

    Lgygl @

    Lgygl @;

    Lgygl @8

    Lgygl ;

    Lgygl 6

    8

    8

    LVI

    MVI

    %8

    8

    LVI

    MVI

    %

    8

    8

    LVI

    MVI

    % 8

    8

    LVI

    MVI

    %

    8

    8

    LVI

    MVI

    %

    i

    Lgygl @ 8Lgygl @%;

    Lgygl @ Lgygl @ ;

    8

    si

    4

    si

    Lgygl 6Lgygl ;

    @

    si

    8 ;8 @si

    88@

    si

    38 @

    si

    =

    si

    -k*

    -h*

    Txgg Stxwctwxgd Knklzsjs Hkne -Txknsiax`* Txgg Stxwctwxgd Szntmgsjs Hkne -Xgcanstxwctjan*@wltjscklg Xgvxgsgntktjan

    Ijbwxg 9? Txgg stxwctwxg ltgx hkne szstg`? -k* djkbxk` ai tmg szstg`, -h* ixg{wgncz xgvxgsgntktjan.

    k ;dj`gnsjankl sjbnkl jnta k 8dj`gnsjankl sjbnkl xgvxgsgntjnb tj`g knd scklg -ljeg ixg{wgncz*

    jniax`ktjan. Tmg jnvwt sjbnkl js xgvxgsgntgd jn tgx`s ai smjitgd knd djlktgd ygxsjans ai k vxatatzvg

    hkndvkss rkyglgt iwnctjan o,n knd smjitgd ygxsjans ai k lar vkss sckljnb iwnctjan o,n, hksgd antmg sckljnb iwnctjan, 6 knd tmg `atmgx rkyglgt hksjs iwnctjan, 6. Tmg xglktjansmjv hgtrggn tmgsgiwnctjans kxg

    uo,n-t* 0 8o!86-8

    ot n*, n _p

    knduo,n-t* 0 8

    o!86-8ot n*, n _p.

    Ta bgngxktg kn kccwxktg `wltjxgsalwtjan yjgr ai tmg jnvwt sjbnkl, tmg iwnctjans 6 knd 6 kxgcmasgn sa tmkt tmgz kxg ai swicjgntlz mjbm axdgx -tzvjckllz dgtgx`jngd g`vjxjckllz* knd canstjtwtg

    kn wncandjtjankl Xjgs hksjs. @axg dgtkjls an tmg vxavgxtjgs ai tmg rkyglgt knd sckljnb iwnctjans

    ckn hg iawnd jn Dkwhgcmjgs U4P knd Ngrlknd U;7, Cmkvtgx ;2P. @wltjxgsalwtjan knklzsjs -@XK*

    xst cajngd hz @kllkt U;8P, cansjsts ai k callgctjan ai ngstgd swhsvkcgs uYopo_ swcm tmkt?

    Yo Yo;.

    @wltjXgsalwtjan knklzsjs vxaogcts tmg sjbnkl }n jnta gkcm ai tmg kvvxa}j`ktjan swhsvkcgs Yo . Tmgkvvxa}j`ktjan sjbnkl js tmgn bjygn hz tmg iallarjnb xglktjansmjv?

    kvvxa}o-t* 0 -VxaoYo}n*-t* 0

    n

    k}-o,n*o,n-t*.

    Tmg cagicjgnts k}-o,e* kxg dgngd tmxawbm tmg jnngx vxadwct ai tmg jnvwt sjbnkl }n rjtm o,n,

    k}-o,n* 0 }n, o,n.

    ;;

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    14/99

    B@;-*

    B6-* M6-*

    M@;-*

    8 8

    8@;

    %}-n* }-n*^

    Knklzsjs ijltgxs Dgc j ktaxs G}vkndgxs Szntmgsjs ijltgxs

    Xgcanstxwctgd

    sjbnkl

    Jnvwt

    sjbnkl

    z@8-n*

    z;-n*B;-*

    B@8-*

    4

    M@8-*

    M;-*

    8@;

    4

    8@;

    8@;

    z6-n*

    z@;-n*

    -k*

    B@;-*

    B6-* M6-*

    M@;-*

    x6 x6

    x@;

    %}-n* }-n*^

    Knklzsjs ijltgxs Dgc j ktaxs G}vkndgxs Szntmgsjs ijltgxs

    Xgcanstxwctgd

    sjbnkl

    Jnvwt

    sjbnkl

    z@8-n*

    z;-n*B;-*

    B@8-*

    x;

    M@8-*

    M;-*

    x@8

    x;

    x@8

    x@;

    z6-n*

    z@;-n*

    -h*

    Ijbwxg 2? Ijltgx hkne stxwctwxgs? -k* tmg g{wjyklgnt nanwnjiax` stxwctwxg ai tmg txgg, -h* tmg bgngxkl

    ltgx hkne stxwctwxg.

    Sj`jlkxlz, tmg dgtkjl sjbnkl js bjygn hz tmg iallarjnb xglktjansmjv?

    dgtkjlo-t* 0 -VxaoRo}n*-t* 0

    n

    d}-o,n*o,n-t*,

    rmgxg tmg cagicjgnts d}-o,n* kxg dgngd tmxawbm tmg jnngx vxadwct ai tmg jnvwt sjbnkl rjtm o,n,

    d}-o,n* 0 }n, o,n.

    Hksgd an tmg khayg, k xgsawxcg sjbnkl ckn hg xgvxgsgntgd rjtmawt lass ai jniax`ktjan wsjnb tmg

    cakxsgst bxkjn kvvxa}j`ktjan sjbnkl knd tmg wndgxlzjnb dgtkjls. Tmjs js smarn jn tmg iallarjnb

    xglktjansmjv?

    XgsawxcgSjbnkl, }n 0 kvvxa}O-t* %O

    o06

    dgtkjlo-t*

    Tmg @XK knklzsjs vxayjdgs ws rjtm bxgkt g}jhjljtz. Rjtm tmjs tzvg ai knklzsjs, ca`hjnktjans

    ai kvvxa}j`ktjans knd dgtkjls ckn hg stwdjgd tabgtmgx ta hgttgx wndgxstknd tmg dznk jcs ai xgsawxcg

    sjbnkls. Ks djscwssgd gkxljgx jn tmg xglktgd raxe sgctjan ai tmjs vkvgx, rg vgxiax`gd kn g`vjxjckl

    stwdz ai tmg vxgdjctkhjljtz ai ngtraxe hkndrjdtm txkcgs U;9P wsjnb tmg Tswnk j taalejt. Jn tmjs

    ;8

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    15/99

    Dgtkjl 6

    Dgtkjl 8

    Dgtkjl ;

    Kvvxa} 6

    Kvvxa} 8

    Kvvxa} ;

    Jnvwt

    Ijbwxg =? @wltjxgsalwtjan knklzsjs ai tmxgg scklgs.

    raxe, rg xst laaegd kt tmg vxgdjctkhjljtz ai tmg dgtkjl sjbnkls knd iawnd tmkt tmgsg sjbnkls kxg djicwlt ta vxgdjct hgckwsg tmgz xgsg`hlg tmkt ai rmjtg najsg, k vxacgss lkcejnb caxxglktjan stxwctwxg.

    Iax kn jnvwt sjbnkl tmkt js astlz lanbxknbg dgvgndgnt -LXD*, k cmkxkctgxjstjc tmkt hjnngd ngtraxe

    hkndrjdtm txkcgs tgnd ta g}mjhjt, jt mks hggn smarn tmkt tmg dgtkjl sjbnkls kxg `astlz tmkt ai rmjtg

    najsg, `kejnb jt djicwlt ta vxgdjct U=P. Tmjs raxe smargd tmjs iax ixkctjankl hxarnjkn `atjan, kn

    LXD vxacgss. Margygx, tmjs vxavgxtz js nat txwg jn bgngxkl, knd g`vjxjckl stwdjgs ckn smgd ljbmt

    an tmg vxgdjctkhjljtz ai tmg dgtkjl sjbnkls iax kn wnsvgcjgd xknda` vxacgss. Ixa` tmg ikjlwxg ai

    vxgdjctkhjljtz an tmg dgtkjl sjbnkls, rg laaegd jnta tmg vxgdjctkhjljtz ai tmg kvvxa}j`ktjan sjbnkls

    knd iawnd tmkt tmgxg g}jsts sa`g vxgdjctkhjljtz. @knz tj`gs tmgxg js k vkxtjcwlkx scklg tmkt vxaygs

    ta hg tmg `ast vxgdjctkhlg, k vmgna`gnan tmkt rg cajn tmg vxgdjctkhjljtz srggt svat. Tmg rkyglgt

    kvvxa}j`ktjan sjbnkls kxg clasglz xglktgd ta hjnnjnb, k tgcmnj{wg ca``anlz g`vlazgd ta laae kttmg `wltjscklg, `wltjixkctkl vxavgxtjgs ai ngtraxe hkndrjdtm txkcgs. Tmg g}jhjljtz ai kn @XK

    knklzsjs js g}txg`glz hgngcjkl ta knklzjnb tmg vxavgxtjgs ai xgsawxcg sjbnkls, knd `kz klsa vxayg

    ta hg j`vaxtknt jn anljng szstg` hwjldjnb.

    4 Bakls knd xg{wjxg`gnts

    Tmg bakl ai Tswnk`j js ta ikcjljtktg tra ksvgcts ai tmg canstxwctjan ai rkyglgthksgd szstg`s iax

    wsg jn djstxjhwtgd szstg`s. Tmg xst js ta vxayjdg k bgngxkl rkyglgt szstg` iax knklzjnb xgsawxcg

    sjbnkls wsjnb `knz djiigxgnt tzvgs ai dgca`vasjtjans knd hksjs iwnctjans. Tmg sgcand js ta wsg

    tmg taalejt jn hwjldjnb anljng ca`vangnts jn djstxjhwtgd szstg`s tmkt lgkd ta vgxiax`kncg bkjns jnvxgdjctjan, djssg`jnktjan knd scklkhjljtz.

    4.; Dgsjbnjnb k rkyglgt szstg` iax xgsgkxcm

    Jn axdgx ta kddxgss tmg bakls ai tmg Tswnk`j taalejt, rg `wst xst wndgxstknd tmg stgvs tmkt k xg

    sgkxcmgx rawld iallar ta wsg rkyglgts ks k taal iax knklzjnb xgsawxcg sjbnkls knd tmgn vxacggdjnb

    ;3

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    16/99

    ta tmg hwjldjnb ai anljng ca`vangngts. Jn rmkt iallars, rg dgscxjhg tmg stgvs k xgsgkxcmgx rawld

    iallar ta kcca`vljsm tmg tkse ai canstxwctjnb kn anljng szstg` wsjnb rkyglgt hksgd tgcmnj{wgs.

    ;. Canstxwct k sgnsax ta `gkswxg tmg xgsawxcg sjbnkl ai jntgxgst. Tmg `gkswxg`gnts `wst hg

    vgxjadjckllz sk`vlgd kt k ngbxkjn xktg swcm tmkt kll j`vaxtknt cmkxkctgxjstjcs ai tmg xgsawxcg

    js ckvtwxgd. Ji tmg xktg js nat ngbxkjn gnawbm, k stxknbg saxt ai kljksjnb `kz accwx, jn tmkttmg jniax`ktjan ckvtwxgd rjll nat hg bxawnd txwtm. Tmg xktg kt rmjcm k xgsawxcg js `gkswxgd

    smawld hg xgsawxcg kvvxavxjktg.

    8. Cxgktg k txkcg lg ixa` tmg sgnsax awtvwt jn axdgx ta ikcjljtktg aijng knklzsjs ai tmg xgsawxcg.

    Tmjs js j`vaxtknt sjncg ang `kz ba tmxawbm `knz txjkls ai knklzsjs.

    3. Dgcjdg wvan tmg jnjtjkl vkxk`gtgxs ai tmg aijng rkyglgt knklzsjs. Tmgsg jnclwdg tmg tzvg

    ai txknsiax`, tmg tzvg ai dgca`vasjtjan, tmg nw`hgx ai lgygls jn tmg dgca`vasjtjan knd tmg

    tzvg ai rkyglgt ltgx. Tmjs stgv `kz hg xgvgktgd `wltjvlg tj`gs sjncg tmgxg kxg dgbxggs ai

    ixggda`.

    4. [wkljtktjyglz ax {wkntjtktjyglz knklzg tmg rkyglgt cagicjgnts wsjnb atmgx aijng vlattjnb

    taals knd knklzsjs taals swcm ks Tswnk j, @ktlkh, bnwvlat ax XVS ta stwdz tmg vxavgxtjgs ai

    tmg awtvwt xgvxgsgntktjan.

    7. @knjvwlktg tmg rkyglgt cagicjgnts wsjnb knz tgcmnj{wg tmkt ang sggs t. G}k`vlgs kxg

    najsg tmxgsmaldjnb hz gxajnb awt lar gngxbz cagicjgnts, djsckxdjnb ykxjaws lgygls jn tmg

    dgca`vasjtjan tmkt kxg dgg`gd wnj`vaxtknt, ax vgxiax`jnb ykxjaws tzvgs ai ca`vxgssjan

    tgcmnj{wgs.

    9. Xgcanstxwct tmg tj`gda`kjn xgsawxcg sjbnkl wsjnb k szntmgsjs stxwctwxg tmkt `ktcmgs tmg

    knklzsjs stxwctwxg jn kn kvvxavxjktg rkz. Vkxk`gtgxs hgtrggn tmg knklzsjs knd szntmgsjsstxwctwxgs smawld hg `ktcmgd jn axdgx ta kyajd wnngcgsskxz gxxax.

    2. Dgtgx jng tmg swccgss ai tmg knklzsjs hz ca`vkxjnb tmg xgcanstxwctgd tj`gda`kjn sjbnkl

    rjtm tmkt ai tmg axjbjnkl xgsawxcg sjbnkl ta ahtkjn ykxjaws vgxiax`kncg `gtxjcs.

    =. Canstxwct kn anljng szstg` wsjnb tmg vkxk`gtgxs ai tmg stwdz rmjcm mkd zjgldgd tmg hgst

    xgswlts, knd cwsta`jg tmg szstg` wsjnb ma`gbxarn salwtjans. Cwsta jgd ca`vangnts

    kxg vlkcgd jn ixant ai tmg knklzsjs sgctjan, hgtrggn tmg knklzsjs knd szntmgsjs sgctjans ax kt

    tmg hkce ai tmg szntmgsjs sgctjan dgvgndjnb stxanblz an tmg kvvljcktjan knd tmg bakls ai tmg

    szstg`.

    K arcmkxt djkbxk` ai tmg vxacgss js smarn vjctaxjkllz jn Ijbwxg :.

    Ta kddxgss ;, tmgxg kxg `knz sgnsaxs tmkt g}jst tadkz ta `gkswxg xgsawxcg sjbnkls jn djstxjhwtgd

    szstg`s. Tmg XVS taalejt vxayjdgs sgnsaxs rmjcm gkswxg mast lakd, ngtraxe hkndrjdtm, Rjndars

    vgxiax`kncg dktk knd !vxac xgsawxcg sjbnkls. Tmg Xg`as U;;P knd tmg Ngtraxe Rgktmgx Sgxyjcg

    -NRS* U89P szstg`s vxayjdg sgnsaxs tmkt `gkswxg kykjlkhlg hkndrjdtm hgtrggn tra gndvajnts. Ji

    tmg szstg` js ta hg wsgd wndgx tmg Rjndars avgxktjnb szstg`, tmg Rktcmtargx U;6P szstg` ckn hg

    g`vlazgd ta `gkswxg mwndxgds ai vgxiax`kncg cawntgxs iax bgngxktjnb `wltjykxjktg, vgxjadjckllz

    ;4

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    17/99

    Canstxwct k sgnsax ta`gkswxg xgsawxcg

    sjbnkl

    Cxgktg txkcg ijlg ixa`sgnsax awtvwt iaxaiiljng knklzsjs

    Cmaasg vkxk`gtgxsiax tmg stwdz

    Xgcanstxwct ixa`

    rkyglgt cagiijcjgnts

    Swccgss1

    Canstxwct kn anljng

    szstg`

    Na

    Zgs

    Xgsgkxcm

    Knklzg xgswltswsjnb vgxiax`kncg

    `gtxjcs

    Knklzg tmg rkyglgtcagiijcjgnts knd

    `knjvwlktgkvvxavxjktglz

    Ijbwxg :? K arcmkxt ai tmg stgvs ai xgsgkxcm wsjnb Tswnk`j.

    Vkxk`gtgx Dgscxjvtjan

    Txknsiax` tzvg Tmg txknsiax tzvg dgcjdgs rmkt ejnd ai dgca`vasjtjan js vgxiax gd. Tmjs ckn

    hg k DRT, stxgk`jnb rkyglgt txknsiax`, rkyglgt vkcegts rjtm gntxavz, wnjiax`

    ltgx hknes, ax avtj`jgd lardglkz ltgx hknes. Tmg txknsiax` ckn klsa hg

    dznk`jckllz cmknbjnb hksgd an tmg sjbnktwxg ai tmg jnca`jnb xgsawxcg sjbnkl.

    Nw`hgx ai lgygls Tmg nw`hgx ai lgygls jn tmg dgca`vasjtjan js tzvjckllz k iwnctjan ai tmg

    txknsiax` tzvg knd tmg ixg{wgncz cmkxkctgxjstjcs ai tmg xgsawxcg sjbnkl ta hg

    knklzgd.

    Rkyglgt hksjs iwnctjan Rmjcm hksjs iwnctjan ta wsg js tzvjckllz dgcjdgd wvan g vjxjckllz. Margygx,

    mjbm axdgx hksjs iwnctjans jncxgksg tmg szstg` dglkz, knd tmgxgiaxg ang rawld

    ljeg ta wsg tmg largst axdgx hksjs iwnctjan rmjlg stjll kcmjgyjnb baad xgswlts.

    Ijbwxg ;6? Tmg dgbxggs ai ixggda` ai k rkyglgt aijng knklzsjs.

    ;7

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    18/99

    sk`vlgd xgsawxcg sjbnkls. Gkcm ai tmgsg wtjljtjgs ckn rxjtg tmg `gkswxg`gnts ai tmg gnyjxan`gnt ta

    lg ta hg wsgd iax aijng knklzsjs, kddxgssjnb jtg` 8.

    Jn jtg` 3, tmgxg kxg `knz tzvgs ai vkxk`gtgxs tmkt ckn hg `knjvwlktgd dwxjnb rkyglgt aijng

    knklzsjs. Ijbwxg ;6 ljsts rmkt rg hgljgyg ta hg tmg dgbxggs ai ixggda` jn aijng knklzsjs. Ang

    `wst xst dgcjdg rmkt tzvg ai txknsiax` js ta hg wsgd. K`anb tmg `ast ca``an txknsiax s kxgtmg DRT, rkyglgt vkcegts, ax knz atmgx tzvg ai ixg{wgncz dgca`vasjtjan xknbjnb ixa` wnjiax`

    ta nanwnjiax` knd ca`hjnktjans hgtrggn. Tmg ng}t vkxk`gtgx ta hg dgtgx`jngd js tmg nw`hgx

    ai lgygls wsgd jn tmg dgca`vasjtjan. K xgsawxcg sjbnkl rmjcm cantkjns mjbm gngxbz jn tmg lar

    ixg{wgncz hknds rjll tzvjckllz rknt ta jncxgksg tmg nw`hgx ai lgygls jn tmg dgca`vasjtjan, lgkdjnb

    ta nkxxar larixg{wgncz hknds. Tmg hksjs iwnctjan wsgd, rmjcm xgvxgsgnts tmg ltgx tzvg knd

    cagicjgnts, kxg tzvjckllz dgtgx jngd g`vjxjckllz. Ang ckn stkxt rjtm k Mkkx rkyglgt -DKWH8*knd jncxgksg tmg ltgx axdgx ljngkxlz ta ahtkjn tmg tzvg ai s`aatmjnb xg{wjxgd iax k bjygn kvvljcktjan.

    Tmgxg kxg `knz dgbxggs ai ixggda` jn k rkyglgt knklzsjs, knd xgsgkxcmgxs dg`knd tmg g}jhjljtz ta

    g}vgxj`gnt rjtm gkcm ai tmgsg vkxk`gtgxs jn tmgjx raxe.

    Jn axdgx ta gyklwktg tmg vkxk`gtgxs wndgx tgst ljstgd jn 4, tmg awtvwt ai tmg knklzsjs -j.g. rkyglgtcagicjgnts ax xgcanstxwctgd sjbnkls* kxg j`vaxtgd jnta atmgx aijng taals iax vgxiax`jnb stktjstjckl

    knklzsjs ax ta laae kt tmg awtvwt ai tmg dgca`vasjtjan jn {wkljtktjyg iksmjan. Taals tmkt rg mkyg

    wsgd iax gyklwktjnb awx vkxk`gtgx cmajcg jnclwdg Tswnk`j, @ktlkh, bnwvlat knd XVS. Bnwvlat js

    k taal tmkt ckn hg wsgd ta vgxiax` sj`vlg bxkvmjnb ai dktk. Margygx, k `axg vargxiwl taal iax

    bxkvmjnb knd klsa vgxiax`jnb tj`gsgxjgs knklzsjs jn k ca`vlgtg vkcekbg js tmg @ktlkh saitrkxg

    ixa` @ktmraxes. Taals swcm ks XVS ckn hg wsgd ta knklzg tmg vxgdjctkhjljtz ai rkyglgt cagi

    cjgnts ta txz knd nd vgxiax`kncg bkjns jn scmgdwljnb `gsskbg txknsigxs aygx ngtraxe ljnes ax

    scmgdwljnb ca`vwtktjan an k sgt ai ckndjdktg masts. Vxgdjctaxs ckn klsa hg g`vlazgd ta kttg`vt ta

    xgdwcg xgkltj`g szstg` dglkz jn tmg szstg`.

    Ks stktgd jn jtg`s 7 knd 9, tmg tzvjckl wsg ai tmg rkyglgt txknsiax` js ta `knjvwlktg tmg cagi

    cjgnts iax k bjygn kvvljcktjan, knd tmgn vgxiax` tmg xgcanstxwctjan. Rmgn hwjldjnb szstg`s tmkt

    wsg tmg rkyglgt txknsiax`, kvvljcktjans kxg tzvjckllz vlkcgd hgtrggn tmg txknsiax hlace knd tmg

    xgcanstxwctjan hlace tmkt salygs sa`g kvxjaxj vwxvasg. Tmjs kvvljcktjan `knjvwlktgs tmg cagi

    cjgnts jn k rkz djctktgd hz tmg kvvljcktjan. Tmg `knjvwlktgd cagicjgnts kxg tmgn xgcanstxwctgd,

    vxadwcjnb kn gstj`ktg ai tmg axjbjnkl xgsawxcg sjbnkl.

    Ks ljstgd jn 2, ta dgtgx`jng tmg swccgss ai tmg sj`wlktjan, k xgsgkxcmgx rjll gyklwktg tmg vgx

    iax`kncg ai k bjygn kvvljcktjan ax stwdz hz ca`vkxjnb tmg axjbjnkl jnvwt xgsawxcg sjbnkl knd tmg

    xgcanstxwctgd xgsawxcg sjbnkl jn tgx`s ai sa`g vgxiax`kncg `gtxjc. Ji tmg `gtxjc dgg`s tmg stwdz

    wnswccgssiwl, tmgn stgv 3 ckn hg xgvgktgd rjtm djiigxgnt vkxk`gtgxs bwjdgd hz tmg yklwg ai tmg vgxiax`kncg `gtxjcs wndgx tgst. Ji tmg stwdz js swccgssiwl, tmgn ks stgv = swbbgsts, k xgsgkxcmgx `kz

    dgcjdg ta hwjld kn anljng szstg` ta vxayjdg gnmkncg`gnts ta tmgjx kvvljcktjan hz tmg jnclwsjan ai

    rkyglgt tgcmnj{wgs.

    Awx bakl js ta vxayjdg k taalha} tmkt kcca`adktgs tmg khayg stgvs. Jn axdgx ta cxgktg k taal

    iax ikcjljtktjnb xgsgkxcm wsjnb rkyglgts, rg mkyg ca`g wv rjtm `knz dgsjbn xg{wjxg`gnts ai k

    rkyglgthksgd xgsgkxcm taalejt.

    ;9

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    19/99

    4.8 Dgsjbn xg{wjxg`gnts ai k rkyglgt-hksgd szstg`

    Ta vxayjdg xgsgkxcmgxs rjtm k vargxiwl rkyglgthksgd taal iax iwxtmgxjnb xgsgkxcm jn tmg wndgx

    stkndjnb ai xgsawxcg sjbnkls knd mar tmgz giigct vgxiax`kncg jn djstxjhwtgd szstg`s, rg mkyg

    ca`vjlgd tmg iallarjnb dgsjbn xg{wjxg`gnts. Tmg xg{wjxg`gnts kxg nat axdgxgd hz j`vaxtkncg, hwt

    xktmgx ixa` larlgygl ta mjbmlgygl khstxkctjans.Bgngxkljtz? Tmg taalejt js dgsjbngd sa tmkt `knz djiigxgnt ca``wnjtjgs ckn wsg Tswnk`j hz

    sj`vlz cxgktjnb k da`kjnhksgd sk`vlg tzvg hksgd an tmgjx kvvljcktjan. Tmjs sk`vlg khstxkctjan

    smawld g}tgnd ta hlaces ai sk`vlgs sa tmkt sk`vlgs `kz hg kbbxgbktgd knd raxegd an jn cmwnes.

    Ca``wnjtjgs tmkt `jbmt hgngt ixa` tmjs taal jnclwdg bxkvmjcs, xahatjcs, ngtraxe szstg`s, jntgx

    kctjyg kxt knd `wsjc.

    Ijng-bxknwlkxjtz ahogcts? Tmg hwjldjnb hlaces ai tmg taalejt smawld hg ngbxkjngd sa tmkt

    `knz djiigxgnt tzvgs ai stxwctwxgs ckn hg canstxwctgd hz kvvxavxjktglz canngctjnb ahogcts tabgtmgx.

    Tmg taal `wst kllar iax kxhjtxkxz dgca`vasjtjans ixa` wnjiax` ta nanwnjiax`, knd klsa txgg

    stxwctwxgs hz tmg cksckdjnb ai trahknd ltgxhknes.

    G}tgnsjhjljtz jn ltgxjnb? @knz djiigxgnt tzvgs ai rkyglgt hksjs iwnctjans -ltgx cagicjgnts*

    smawld hg swvvaxtgd, ks rgll ks djiigxgnt tzvgs ai ltgxs swcm ks njtg j`vwlsg xgsvansg ltgxs -IJX*

    knd jnnjtg j`vwlsg xgsvansg ltgxs -JJX*. Jt smawld hg gksz ta kdd ngr ltgxs ta tmg taalejt ks tmg

    nggd kxjsgs.

    @wltjvljcjtz jn avgxktjan? Avgxktjans jn tmg taalejt smawld xwn jn sk`vlg hz sk`vlg `adg, ax

    jn hlace `adg hz tmg kbbxgbktjan ai sk`vlgs jnta hlaces. @gcmknjs`s smawld hg cxgktgd rmjcm

    kllar tmg wsgx ta kbbxgbktg sk`vlgs jnta k hlace knd ckll hlace avgxktjans, ax clace sk`vlgs jnta

    sk`vlg avgxktjan `gtmads. Jn tmg txknsiax`ktjans, stktg smawld hg egvt sa tmkt k wsgx ckn srjtcm

    hgtrggn sk`vlg knd hlace avgxktjan kt g}gcwtjan tj`g hz cklljnb tmg caxxgct `g`hgx iwnctjan.

    Stxgk`jnb avgxktjan? Rg dgng stxgk`jnb avgxktjan ks tmg khjljtz ta clace sk`vlgs ax hlaces

    ai sk`vlgs jnta tmg stxwctwxg ai tmg dgca`vasjtjan ks saan ks tmgz kxg xgkdz knd mkyg tmg` clace

    awt ks tmgz mkyg hggn vxacgssgd. Stxgk`jnb avgxktjan txgkts tmg rkyglgt stxwctwxg ks k ltgx hknejnstgkd ai owst kn klbaxjtm` ks js tmg cksg rjtm tmg DRT. Rmgn hwjldjnb anljng szstg`s wsjnb

    rkyglgts, stxgk`jnb avgxktjan js kn jnyklwkhlg tgcmnj{wg rmgn dglkz canstxkjnts kxg swcm tmkt jt js

    jnkvvxavxjktg ta rkjt iax k hlace ai sk`vlgs. Tmjs sjtwktjan kxjsgs ixg{wgntlz jn jntgxkctjyg szstg`s

    knd `knz tj`gs jn djstxjhwtgd szstg`s rjtm xgkltj`g canstxkjnts.

    Ca`vktjhjljtz rjtm atmgx taals? Tmg djscxgtg rkyglgt txknsiax` -DRT* knd tmg jnygxsg djs

    cxgtg rkyglgt txknsiax` -JDRT* smawld hg swvvaxtgd. Jn tmjs tzvg ai txknsiax`, kn jnvwt hwiigx js

    vxayjdgd, lgnbtm 8@, zjgldjnb kn awtvwt sjbnkl cansjstjnb ai@% ; lgygls, lgnbtm 8@. Tmg vkxk`gtgx @ js tmg nw`hgx ai trahknd ltgx hknes, k stxwctwxg tmkt rg laasglz tgx` k stkbg, wsgd jn tmgtxknsiax`ktjan. Sjncg jt js wndgngd ta xwn tmg DRT!JDRT jn stxgk`jnb sk`vlg avgxktjan, tmjs

    rjll anlz swvvaxt hlace avgxktjans.Ilg}jhjljtz jn @XK? Jntgxikcgs smawld hg canstxwctgd ta ahtkjn tmg kvvxa}j`ktjan knd dgtkjl

    sjbnkls. Knz ca`hjnktjan ai tmg tra tzvgs ai sjbnkls smawld klsa hg swvvaxtgd.

    Kdkvtkhjljtz? Tj`g ykxzjnb avgxktjan smawld hg gksjlz kcmjgygd tmxawbm `gcmknjs`s ai tmg

    dgsjbn. Tmg Tswnk`j dgsjbn smawld swvvaxt cmknbjnb tmg nw`hgx ai hknds jn tmg dgca`vasjtjan,

    cmknbjnb tmg dgca`vasjtjan tzvg, knd cmknbjnb tmg tzvg ai ltgxs wsgd jn tmg dgca`vasjtjan kt

    xwntj`g. Tmjs kllars k xgsgkxcmgx ta kdkvt tmg stxwctwxg ai tmg knklzsjs hksgd an jnvwt sjbnkl

    dznk`jcs.

    ;2

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    20/99

    Jntgxavgxkhjljtz? Tmg Tswnk`j taalejt `wst caxxgctlz jntgxikcg ta XVS, j`vlzjnb tmkt tmg sgn

    sax awtvwts ixa` XVS `wst hg canygxtgd ta sk`vlgs tmkt Tswnk`j ckn wndgxstknd, knd tmgn hkce

    kbkjn. Tmg jntgxikcgs `wst mkyg tmg khjljtz ta hg sgxjkljgd aygx tmg ngtraxe wsjnb XVSs `jxxax

    khstxkctjan.

    Ojttgx jnsgnsjtjyjtz? Tmg taal smawld hg khlg ta xgcaygx ixa` ojttgx knd last sk`vlgs dwg ta

    tmg jnikllkhjljtz ai tmg ngtraxe. Xgcaygxz smawld kttg`vt ta da sa`gtmjnb xgksankhlg swcm ksjntgxvalktjan -gssgntjkllz kygxkbjnb* ax sj`vlz gxajnb last sk`vlgs. Ji sk`vlgs tmkt kxxjyg lktg

    mkyg klxgkdz hggn kccawntgd iax, tmg jniax`ktjan jn tmg lktg kxxjyjnb sk`vlg ckn hg wsgd jn tmg ng}t

    ojttgx kctjan gygnt tmkt tkegs vlkcg.

    Jn tmg ng}t sgctjan, rg smar mar ta ahtkjn, ca`vjlg knd wsg Tswnk`j j``gdjktglz ks kn

    knklzsjs taal. Xgkdgxs rma rjsm ta wndgxstknd tmg saitrkxg j`vlg`gntktjan hgiaxg wsjnb tmg taal,

    ckn sejv ta Sgctjan 9 knd lktgx xgtwxn ta tmg ng}t sgctjan iax wskbg dgtkjls.

    7 Wsjnb Tswnk`j awt ai tmg ha}

    Rg mkyg hwjlt `knz ca``knd ljng wtjljtjgs tmkt kllar xgsgkxcmgxs ta j``gdjktglz wsg Tswnk j kitgxjt mks hggn darnlakdgd knd ca`vjlgd. Tswnk j js `kdg kykjlkhlg tmxawbm tmg xglgksg ai XVS 8.

    Ancg tmg xglgksg vkcekbg mks hggn darnlakdgd knd g}txkctgd ixa` tmg tkx lg jnta tmg wsgx dgngd

    xaat djxgctaxz, kll dacw`gntktjan xglktgd ta tmg szstg` hwjld js lacktgd jn tmg djxgctaxz dac. Tmg

    lg HWJLD vxayjdgs kn g}vlknktjan an mar ta sgt tmg gnyjxan`gnt iax kn XVS hwjld knd mar ta

    ca`vjlg tmg cadg iax k bjygn hwjld gnyjxan`gnt. Tmg Tswnk`j taalejt js mjbmlz dgvgndgnt an tmg

    XVS hwjld gnyjxan`gnt, knd tmg stgvs awtljngd jn tmg HWJLD dacw`gnt `wst hg iallargd jnjtjkllz.

    Ancg tmgsg stgvs kxg ca`vlgtgd, [email protected] vxayjdgs kn g}vlknktjan an mar ta hwjld

    tmg Tswnk`j taalejt kitgx kll atmgx hwjld dgvgndgncjgs mkyg hggn sktjsgd.

    Tmg Tswnk`j ljhxkxz js hwjlt ixa` tmg Rkyglgts djxgctaxz lacktgd ks k swhdjxgctaxz ai tmg XVS

    xaat djxgctaxz. Tmg djxgctaxz stxwctwxg lacktgd jn tmjs djxgctaxz iallars ixa` tmg hwjld gnyjxan`gntai XVS. Tmg sawxcg cadg iax tmg taalejt js lacktgd jn tmg jnclwdg knd sxc djxgctaxjgs. Kitgx

    swccgssiwl ca`vjlktjan, tmg ca``knd ljng wtjljtjgs rjll hg jn tmg djxgctaxz

    Rkyglgts!hjn!$XVSQKXCM!$XVSQAS

    kccgssgd ixa` tmg xaat djxgctaxz ai tmg xglgksg. Tmg gnyjxan`gnt ykxjkhlgs $XVS KXCM knd

    $XVS AS dgscxjhg tmg kxcmjtgctwxg ai tmg `kcmjng knd tmg avgxktjnb szstg` xgsvgctjyglz. Tmgsg

    gnyjxan`gnt ykxjkhlgs kxg kxtjikcts ai xglgksjnb Tswnk`j rjtm XVS knd `kz hg cmknbgd jn iwtwxg

    xglgksgs ta jts arn jndgvgndgnt vxaogct.

    Jn tmjs sgctjan, rg vxayjdg g}k`vlgs ai mar ta bgt stkxtgd wsjnb Tswnk`j rjtmawt lgkxnjnb `ast

    ai tmg dgtkjls nggdgd ta g}tgnd knd hwjld kdykncgd kvvljcktjans rjtm awx taalejt. Iax k djscwssjanan `axg kdykncgd wskbg knd g}tgnsjans ta tmg taalejt, rg xgigx tmg xgkdgx ta Sgctjan 2. Jn Ijbwxg ;;

    rg ljst tmg stktjckllz stxwctwxgd, stxgk`jnb wtjljtjgs tmkt rg vxayjdg. K`anb tmgsg, rg mkyg wtjljtjgs

    tmkt ca`vwtg tmg iaxrkxd txknsiax`ktjans vxayjdjnb rkyglgt cagicjgnts knd @XK cagicjgnts

    ks rgll ks tmg xgygxsg txknsiax`ktjans tmkt vgxiax` tmg xgcanstxwctjan ixa` rkyglgt cagicjgnts.

    Gkcm ai tmgsg wtjljtjgs ckn hg xwn an jndjyjdwkl sk`vlgs ax an k hlace ai sk`vlgs. Klsa, k `j}

    8Ta darnlakd tmg lktgst ygxsjan ai Tswnk`j, vlgksg yjsjt tmg XVS rghsjtg lacktgd kt

    mttv?!!rrr.cs.naxtmrgstgxn.gdw!XVS!

    ;=

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    21/99

    Wtjljtz Nk`g Dgscxjvtjan

    Stxgk`jnb Stktjc Iaxrkxd Txknsiax`s

    sk vlg stktjc sirt Iaxrkxd stktjc txknsiax` wtjljtz tmkt vxayjdgs kvvxa}j`ktjan,

    dgtkjl knd txknsiax` sjbnkls jn sk`vlg avgxktjan

    hlace stktjc sirt Sk`g ks khayg jn sk`vlg hlace avgxktjan

    sk`vlg stktjc `j}gd sirt Iaxrkxd stktjc txknsiax tmkt vxayjdgs k `j} ai kvvxa}j`ktjanknd dgtkjl sjbnkls hksgd an k sjbnkl svgcjcktjan

    hlace stktjc `j}gd sirt Sk g ks khayg jn sk vlg hlace avgxktjan

    Stxgk`jnb Stktjc Xgygxsg Txknsiax`s

    sk vlg stktjc sxrt Xgygxsg stktjc txknsiax` wtjljtz tmkt xgcanstxwcts tmg t j g

    da`kjn sjbnkl ixa` rkyglgt cagicjgnts

    hlace stktjc sxrt Sk`g ks khayg jn sk`vlg hlace avgxktjan

    sk`vlg stktjc `j}gd sxrt Xgcanstxwctjans wsjnb k `j} ai kvvxa}j ktjan knd dgtkjl

    sjbnkls hksgd an k sjbnkl svgcjcktjan. @kz vxadwcg gxxax

    hgtrggn jnvwt sjbnkl knd xgcanstxwctjan hksgd an `j} ai jnvwt

    sjbnkls

    hlace stktjc `j}gd sxrt Sk g ks khayg jn sk vlg hlace avgxktjan

    Stxgk`jnb Stktjc Szstg` Tgsts

    sk`vlg stktjc stxgk`jnb tgst Tmjs wtjljtz vgxiax s k stktjc iaxrkxd txknsiax knd tmgn

    xgcanstxwcts wsjnb k dglkz hlace knd k xgygxsg txknsiax`. Kn

    gxxax sjbnkl js bgngxktgd ta smar tmg szstg` js raxejnb

    caxxgctlz. Gxxax smawld hg ngbljbjhlg

    hlace stktjc stxgk jnb tgst Sk`g ks khayg jn sk`vlg hlace avgxktjan

    Ijbwxg ;;? Tswnk`j stxgk`jnb stktjc txknsiax` ca``knd ljng wtjljtjgs

    ai kvvxa}j`ktjans knd dgtkjls ckn hg xg{wgstgd hz wsjnb tmg `j}gd sjbnkl wtjljtjgs. Tgst cadg js

    vxayjdgd iax dgtgx`jnjnb rmgtmgx tmg xawtjngs kxg raxejnb caxxgctlz kitgx tmg hwjld, knd xgkllzvxayjdg na knklztjckl hgngts. Tmg tgst xawtjngs ca`vwtg tmg gxxax hgtrggn kn jnvwt sjbnkl knd tmg

    xgcanstxwctgd sjbnkl. Tmg gxxax smawld hg ngbljbjhlg ji tmg taalha} mks hggn jnstkllgd caxxgctlz.

    Jn Ijbwxg ;8 rg ljst tmg dznk`jc stxgk`jnb wtjljtjgs. Tmg dznk`jc txknsiax`s kxg sj`jlkx ta tmg

    stktjc txknsiax`s g}cgvt tmkt tmg stxwctwxg ai tmg dgca`vasjtjan knd tmg cagicjgnts wsgd ckn hg

    cmknbgd dznk`jckllz kt xwntj`g. Tmg wtjljtjgs ljstgd mgxg kxg g}txg`glz sj`vlg jn tmkt tmg cmknbgs

    mkvvgn kt vgxjadjc vajnts jn tj`g jn tgx`s ai tmg nw`hgx ai sk`vlgs. K `axg savmjstjcktgd kv

    vljcktjan `jbmt dgtgct gvacm cmknbgs jn tmg jnvwt sjbnkl knd smkvg tmg stxwctwxg ax cmknbg tmg

    cagicjgnts kccaxdjnblz. Tmjs js kn kxgk tmkt rg mkyg bjygn sa`g tmawbmt ta, hwt rg da nat vxayjdg

    sjbnkl dgtgctjan iwnctjankljtz jn tmg cwxxgnt xglgksg ai tmg taalejt.

    Jn Ijbwxg ;3 rg ljst tmg djscxgtg rkyglgt txknsiax` wtjljtjgs. Tmgsg wtjljtjgs kxg k hjt djiigxgntixa` tmg atmgxs jn tmkt tmg txknsiax js anlz ta hg xwn jn hlace `adg, knd tmg hlace sjg js k iwnctjan

    ai tmg jnvwt sjbnkl lgnbtm. Avgxktjans swcm ks iaxrkxd, xgygxsg knd `j}gd kxg swvvaxtgd jn k sj`jlkx

    `knngx ta tmkt ai tmg stktjc stxgk`jnb knd dznk`jc stxgk`jnb txknsiax`s.

    Tmg kxbw`gnts ai gkcm ai tmgsg wtjljtjgs kxg djiigxgnt hksgd an tmg tzvg ai avgxktjan. Rg mkyg

    xgcabnjgd sgygn clkssgs ai ca``knd ljng kxbw`gnts. Tmgsg kxg hksjc stktjc stxgk`jnb, `j}gd

    stktjc stxgk`jnb, hksjc dznk`jc stxgk`jnb, `j}gd dznk`jc stxgk`jnb, hksjc djscxgtg, gxall djs

    cxgtg knd `j}gd djscxgtg ca``knd ljng kxbw`gnts. Jn Ijbwxg ;4, rg ca`vjlg k ljst ai rmjcm wtjljtjgs

    ;:

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    22/99

    Wtjljtz Nk`g Dgscxjvtjan

    Stxgk`jnb Iaxrkxd Dznk`jc Txknsiax`s

    sk`vlg dznk`jc sirt Iaxrkxd dznk`jc txknsiax` wtjljtz tmkt vxayjdgs

    kvvxa}j`ktjan, dgtkjl knd txknsiax` sjbnkls jn

    sk`vlg avgxktjan. Stxwctwxg knd ltgx cmknbgs

    svgcjgd ks k sk`vlg jntgxykl wvan rmjcm ta kdkvthlace dznk`jc sirt Sk`g ks khayg jn sk`vlg hlace avgxktjan

    sk`vlg dznk`jc `j}gd sirt Iaxrkxd dznk`jc txknsiax tmkt vxayjdgs k `j} ai

    kvvxa}j`ktjan knd dgtkjl sjbnkls hksgd an k sjbnkl

    svgcjcktjan. Cmknbgs accwx hksgd an sk`vlg cmknbg

    jntgxykl.

    hlace dznk jc `j}gd sirt Sk`g ks khayg jn sk vlg hlace avgxktjan

    Stxgk`jnb Xgygxsg Dznk`jc Txknsiax`s

    sk vlg dznk jc sxrt Xgygxsg dznk`jc txknsiax` wtjljtz tmkt xgcanstxwcts

    tmg tj`gda`kjn sjbnkl ixa` tmg iaxrkxd txknsiax`.

    Wvan k iaxrkxd txknsiax` dznk`jc cmknbg, tmg xgygxsg

    txknsiax` `wst cmknbg sj`jlkxlz. Cmknbg jntgxykl js

    vkssgd ks kn kxbw`gnt

    hlace dznk`jc sxrt Sk`g ks khayg jn sk`vlg hlace avgxktjan

    sk`vlg dznk`jc `j}gd sxrt Xgcanstxwctjans wsjnb k `j} ai kvvxa}j`ktjan knd

    dgtkjl sjbnkls hksgd an k sjbnkl svgcjcktjan.

    Cmknbg jntgxykl js vkssgd ks kn kxbw`gnt. @kz vxadwcg

    sa`g gxxax hksgd an jnvwt sjbnkls

    hlace dznk jc `j}gd sxrt Sk`g ks khayg jn sk vlg hlace avgxktjan

    Stxgk`jnb Dznk`jc Szstg` Tgsts

    sk`vlg dznk`jc stxgk jnb tgst Tmg szstg` tgst vgxiax s k iaxrkxd dznk`jc

    txknsiax` iallargd hz tmg kvvxavxjktg

    dglkz ca`vangnt knd tmg xgygxsg dznk`jc

    txknsiax`. Tmg stxwctwxgs ai tmg iaxrkxd kndxgygxsg cmknbg kccaxdjnb ta k sk`vlg jntgxykl

    vkssgd ks kn kxbw`gnt.

    hlace dznk`jc stxgk jnb tgst Sk`g ks khayg jn sk`vlg hlace avgxktjan

    Ijbwxg ;8? Tswnk`j stxgk`jnb dznk`jc txknsiax` ca``knd ljng wtjljtjgs

    hglanb ta rmjcm clkss. Tmg clkss dgsjbnktjans kxg xgvxgsgntgd mjgxkxcmjckllz jn Ijbwxg ;7.

    Tmg hksjc ca``knd ljng kxbw`gnts iax tmg stxgk`jnb stktjc txknsiax`s jn tmg iaxrkxd knd

    xgygxsg djxgctjan iallar tmg iax`

    .!hksjcQstktjcQstxgk`jnb UjnvwtijlgP UrkyglgttzvgjnjtP

    Unw`stkbgsjnjtP Utxknsiax`tzvgP UilktP UawtvwtijlgP.

    Rmgn tmg ca``knd js ai k `j}gd sjbnkl tzvg, k ca`hjnktjan ai kvvxa}j`ktjan knd dgtkjl

    sjbnkls, kn kddjtjankl sjbnkl svgcjcktjan lg js xg{wjxgd jn tmg kxbw`gnt ljst. Tmg iax`kt ai tmg

    sjbnkl svgcjcjktjan lg js sj`vlg, knd ks kn g}k`vlg rg smar tmg szntk} iax k wsgx xg{wgstjnb yg

    kvvxa}j`ktjan sjbnkls knd yg dgtkjl sjbnkls. Tmg sjbnkl svgcjcktjan lg mks tmg iax`?

    86

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    23/99

    Wtjljtz Nk`g Dgscxjvtjan

    Djscxgtg Txknsiax`s

    djscxgtg iaxrkxd txknsiax` Tmjs wtjljtz vgxiax s tmg djscxgtg rkyglgt txknsiax an k hlace

    ai sk`vlgs lgnbtm 8@. Jt ckn vxayjdg tmg kvvxa}j`ktjan,dgtkjl knd txknsiax` sjbnkls ixa` tmg avgxktjan

    djscxgtg xgygxsg txknsiax` Tmjs wtjljtz canygxts tmg gncadgd hlace ai rkyglgt cagicjgntshkce jnta tmg tj`gda`kjn sjbnkl.

    djscxgtg xgygxsg gxall txknsiax Sk`g ks khayg, hwt gxalls lgygls kccaxdjnb ta k gxa

    svgcjcktjan

    djscxgtg iaxrkxd `j}gd Tmjs wtjljtz vgxiax s tmg djscxgtg rkyglgt txknsiax knd

    vxayjdgs k `j} ai kvvxa}j`ktjan knd dgtkjl sjbnkls hksgd an tmg

    sjbnkl svgcjcktjan

    djscxgtg xgygxsg `j}gd Tmjs wtjljtz canygxts hkce jnta tmg tj gda`kjn sjbnkl wsjnb k

    `j} ai kvvxa}j`ktjan knd dgtkjl sjbnkls. Tmgxg `kz hg sa`g

    gxxax jnyalygd jn tmjs avgxktjan

    Djscxgtg Txknsiax` Szstg` Tgsts

    djscxgtg txknsiax tgst Vgxiax s k djscxgtg rkyglgt txknsiax iallargd hz k xgygxsg

    djscxgtg rkyglgt txknsiax`. Tmg jnvwt knd awtvwt ai tmjs

    avgxktjan smawld hg g{wjyklgnt

    Ijbwxg ;3? Tswnk`j djscxgtg rkyglgt txknsiax` ca``knd ljng wtjljtjgs

    Sjbnkl Svgcjijcktjan Ijlg Iax`kt# Sjbnkl tzvg iallargd hz rmjtgsvkcg iallargd hz tmg nw`hgx ai

    # lgygls jn tmg svgcjijcktjan knd tmg lgygl nw`hgxs. Tmjs js

    # wsgd iax `j}gd sjbnkl txknsiax`s. Ca``gnts kxg dgsjbnktgd

    # hz tmg # sjbn. Tmg iax` js?

    # TZVG NW@LGYGLS LGYGLNW@HGXS

    KVVXA] 7 6 ; 8 3 4 # sgt ai kvvxa}j`ktjan lgyglsDGTKJL 7 6 ; 8 3 4 # sgt ai dgtkjl lgygls

    Ji tmg xg{wgstgd sjbnkl lgygls da nat `keg sgnsg hksgd an tmg tatkl nw`hgx ai stkbgs jnvwt ta tmg

    ca``knd ljng wtjljtz, tmgn tmg lgygls tmkt ckn hg sktjsgd kxg xgtwxngd ta tmg wsgx. Jn tmgsg tzvgs

    ai avgxktjans, tmg txknsiax` tzvg mks hggn g}clwdgd sjncg kn @XK knklzsjs js kssw`gd hz tmg

    kddjtjan ai tmg sjbnkl svgcjcktjan. Tmg ca``knd ljng kxbw`gnts iax k `j}gd txknsiax` mks tmg

    iax`

    .!`j}gdQstktjcQstxgk`jnb UjnvwtijlgP UrkyglgttzvgjnjtP

    Unw`stkbgsjnjtP UsvgcjijcktjanijlgP UilktP UawtvwtijlgP.

    Tmg stxgk`jnb dznk`jc txknsiax`s mkyg kddjtjankl kxbw`gnts aygx tmg stktjc txknsiax`s jn

    axdgx ta svgcjiz tmg ixg{wgncz rjtm rmjcm tmg stxwctwxg knd ltgx cagicjgnts smawld cmknbg. Tmg

    ca``knd ljng kxbw`gnts iax tmg dznk`jc wtjljtjgs iallar tmg iax`

    .!hksjcQdznk`jcQstxgk`jnb UjnvwtijlgP UrkyglgttzvgjnjtP

    Unw`stkbgsjnjtP Utxknsiax`tzvgP UrkyglgttzvgngrP

    Unw`stkbgsngrP UcmknbgjntgxyklP UilktP UawtvwtijlgP.

    8;

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    24/99

    Kxbw`gnt clkss knd ljst ai wtjljtjgs

    Hksjc stktjc stxgk`jnb

    sk`vlg stktjc sirt

    hlace stktjc sirt

    sk`vlg stktjc sxrt

    hlace stktjc sxrtsk`vlg stktjc stxgk`jnb tgst

    hlace stktjc stxgk`jnb tgst

    @j}gd stktjc stxgk`jnb

    sk`vlg stktjc `j}gd sirt

    hlace stktjc `j}gd sirt

    sk`vlg stktjc `j}gd sxrt

    hlace stktjc `j}gd sxrt

    Hksjc dznk`jc stxgk`jnb

    sk`vlg dznk`jc sirt

    hlace dznk`jc sirt

    sk`vlg dznk`jc sxrt

    hlace dznk`jc sxrt

    sk`vlg dznk`jc stxgk`jnb tgst

    hlace dznk`jc stxgk`jnb tgst

    @j}gd dznk`jc stxgk`jnb

    sk`vlg dznk`jc `j}gd sirt

    hlace dznk`jc `j}gd sirt

    sk`vlg dznk`jc `j}gd sxrt

    hlace dznk`jc `j}gd sxrt

    Hksjc djscxgtg

    djscxgtg iaxrkxd txknsiax`

    djscxgtg xgygxsg txknsiax`

    djscxgtg txknsiax` tgst_gxall djscxgtg

    djscxgtg xgygxsg gxall txknsiax`

    @j}gd djscxgtg

    djscxgtg iaxrkxd `j}gd

    djscxgtg xgygxsg `j}gd

    Ijbwxg ;4? Kxbw`gnt clkssgs knd caxxgsvandjnb Tswnk`j wtjljtjgs

    Ks khayg, ji tmg txknsiax` js ai tmg `j}gd tzvg knd dznk`jc, tmgn tmg ca``knd ljng kxbw`gnts

    iax tmgsg tzvg ai wtjljtgs iallar tmg iax`

    .!`j}gdQdznk`jcQstxgk`jnb UjnvwtijlgP UrkyglgttzvgjnjtP

    Unw`stkbgsjnjtP UsvgcjijcktjanijlgP UrkyglgttzvgngrP

    Unw`stkbgsngrP UcmknbgjntgxyklP UilktP UawtvwtijlgP.

    Tmg dznk`jc `j}gd txknsiax`s cawld mkyg kn kddjtjankl sjbnkl svgcjcktjan iax gkcm stxwctwxg

    jntgxykl, hwt kt tmjs tj`g rg mkyg vxayjdgd owst tmg hksg dznk`jc avgxktjan. Jt js k sj`vlg g}tgnsjan

    tmkt xg{wjxgs ygxz ljttlg kddjtjankl cadg ta kdd tmjs iwnctjankljtz.

    88

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    25/99

    Ca``knd ljng clkssgs

    Djscxgtg Stxgk`jnb

    Hksjc @j}gd

    Stktjc Dznk`jcStktjc Dznk`jc

    Hksjc @j}gd_gxaijll

    Ijbwxg ;7? Ca``knd ljng wtjljtz clkss mjgxkxcmz.

    Tmg djscxgtg rkyglgt txknsiax`s kctwkllz xg{wjxg lgss kxbw`gnts tmkn tmg stxgk`jnb txknsiax`s.

    Tmjs js dwg ta tmg ikct tmkt tmg nw`hgx ai stkbgs kxg jnigxxgd ixa` tmg lgnbtm ai tmg jnvwt lg. Tmg

    ca``knd ljng kxbw`gnts iax txknsiax`s ai tmjs tzvg iallar tmg iax`

    .!hksjcQdjscxgtg UjnvwtijlgP UrkyglgttzvgjnjtPUtxknsiax`tzvgP UilktP UawtvwtijlgP.

    K xgygxsg txknsiax`ktjan rjtm sa`g ai tmg lgygls gxallgd js swvvaxtgd hz tmg taalejt. Tmjs

    tzvg ai xgygxsg txknsiax` xg{wjxgs k gxall svgcjcktjan lg tmkt dgsjbnktgs rmjcm lgygls kxg ta

    hg gxa llgd hgiaxg vgxiax`jnb tmg xgygxsg txknsiax`ktjan. Tmg lg iax`kt js sj`jlkx ta tmkt ai

    tmg sjbnkl svgcjcktjan lg smarn gkxljgx. Jt cantkjns k gxall dgsjbnktax, tmg nw`hgx ai lgygls ta

    gxa knd tmg lgygl nw`hgxs. Kn g}k`vlg ai gxajnb awt lgygls 6, ;, 4 knd 7 kxg smarn ks iallars?

    _gxa-ijll Svgcjijcktjan Ijlg Iax`kt

    # Tmjs js tmg gxa svgcjijcktjan ijlg iax vgxiax`jnb

    # gxa ijll xgygxsg txknsiax`s. Tmg iax` js?

    # _GXAQDGSJB NW@LGYGLS LGYGLNW@HGXS

    _ 4 6 ; 4 7 # _gxa awt lgygls 6, ;, 4 knd 7

    Rmgn wsjnb tmg djscxgtg xgygxsg txknsiax` rjtm tmg gxalljnb ai svgcjc dgsjbnktgd lgygls, tmg

    ca``knd ljng kxbw`gnts iallar tmg iax`

    .!gxaijllQdjscxgtg UjnvwtijlgP UrkyglgttzvgjnjtP

    UgxasvgcijlgP Utxknsiax`tzvgP Utxknsiax`tzvgP UilktP

    UawtvwtijlgP.

    Tmg djscxgtg txknsiax` ckn klsa hg xwn jn `j}gd `adg, rmjcm jn tmkt cksg jt rawld hg xwn

    rjtm tmg kddjtjan sjbnkl svgcjcktjan kxbw`gnt. Tmg ca``knd ljng kxbw`gnts iax `j}gd sjbnklca``knds ai tmjs tzvg iallar tmg iax`

    .!`j}gdQdjscxgtg UjnvwtijlgP UrkyglgttzvgjnjtP

    UsvgcjijcktjanijlgP UilktP UawtvwtijlgP.

    Jn Ijbwxg ;9, k dgscxjvtjan ai tmg kxbw`gnts tmkt rg swvvaxt iax stktjc knd dznk`jc stxgk`jnb

    txknsiax`s knd tmg djscxgtg hlace txknsiax`s kxg smarn. Tmg bwxg ljsts tmg kxbw`gnt clkssgs knd

    83

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    26/99

    Stxgk`jnb Djscxgtg

    Stktjc Dznk`jc

    Kxbw`gnt Dgscxjvtjan Hksjc @j}gd Hksjc @j}gd Hksjc @j}gd _gxall

    jnvwtlg Iax`kttgd jnvwt lg zgs zgs zgs zgs zgs zgs zgs

    ai sk`vlgs

    rkyglgttzvgjnjt Tmg rkyglgt hksjs zgs zgs zgs zgs zgs zgs zgsiwnctjan ta wsg

    nw`stkbgsjnjt Tmg nw`hgx ai lgygls zgs zgs zgs zgs na na na

    jn tmg dgca`vasjtjan

    txknsiax`tzvg Kvvxa}j`ktjan anlz zgs zgs zgs zgs zgs zgs zgs

    -KVVXA]*, Dgtkjl anlz

    -DGTKJL*, ax Txknsiax`

    -TXKNSIAX@*

    svgcjcktjanlg Wsgd iax j}gd sjbnkls na zgs na zgs na zgs na

    ta svgcjiz rmjcm

    kvvxa}j`ktjans knd

    dgtkjls ta awtvwt

    gxasvgclg Wsgd iax gxalljnb na na na na na na zgs

    lgygls jn djscxgtg

    xgygxsg txknsiax`s

    awtvwtlg Iax`kttgd awtvwt lg zgs zgs zgs zgs zgs zgs zgs

    ai rkyglgt cagicjgnts

    ax xgcanstxwctgd

    sk`vlgs

    kt Dgsjbnktgs rmgtmgx tmg zgs zgs zgs zgs zgs zgs zgs

    awtvwt smawld hg mw`kn

    xgkdkhlg ax nat

    rkyglgttzvgngr Tmg rkyglgt hksjs na na zgs zgs na na na

    iwnctjan ta dznk`jckllzsrjtcm jnta vlkcg

    nw`stkbgsngr Tmg ngr nw`hgx ai na na zgs zgs na na na

    stkbgs ta dznk`jckllz

    srjtcm ta

    cmknbgjntgxykl Tmg k`awnt ai tj`g jn na na zgs zgs na na na

    sk`vlgs hgiaxg

    cmknbjnb ta tmg ngr

    rkyglgt tzvgs knd

    nw`hgx ai stkbgs

    Ijbwxg ;9? Tswnk`j ca``knd ljng kxbw`gnts

    rmjcm kxbw`gnts hglanb ta gkcm clkss. Jn tmg clkss ljst, zgs j`vljgs tmkt tmg kxbw`gnt js xg{wjxgd iax

    tmkt clkss ai jnvwt kxbw`gnts rmjlg na j`vljgs tmg avvasjtg. Ixa` tmg tra bwxgs, jt js j`vaxtknt ta

    natg tmkt awx szstg` tgst cadgs knd xgygxsg txknsiax`s hglanb ta tmg hksjc kxbw`gnt clkssgs hwt anlz

    tkeg TXKNSIAX@ ks tmg txknsiax`tzvg. Tmg tgst wtjljtz js ta ahsgxyg tmg vgxigct xgcanstxwctjan

    vxavgxtz ai tmg txknsiax`, knd iax tmg xgygxsg txknsiax` wtjljtjgs jt dagsnt `keg `wcm sgnsg ta

    84

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    27/99

    xgcanstxwct wsjnb anlz dgtkjl ax kvvxa}j`ktjan sjbnkls.

    Ta vxayjdg tmg xgkdgx rjtm k kyax ai k sk`vlg wtjljtz, jn tmg iallarjnb rg smar tmg sawxcg

    cadg ai ang ai tmg hksjc szstg` tgsts, tmg sk`vlg stktjc stxgk`jnb tgst`adwlg. Rg cmaasg ta smar

    tmjs cadg hgckwsg jt dg`anstxktgs mar ta wsg tmg stxgk`jnb iaxrkxd txknsiax`s, tmg dglkz hlace

    xg{wjxgd iax vgxigct xgcanstxwctjan jn k stxgk`jnb txknsiax` knd tmg stxgk`jnb xgygxsg txknsiax`s.Tmjs wtjljtz ks rgll ks kll atmgx wtjljtjgs kxg rxjttgn jn tmg C%% vxabxk``jnb lknbwkbg.

    Wskbg iax wtjljtzyajd wskbg-*

    u

    cmkx /th0BgtTswnk`jHknngx-*5

    cmkx /h0BgtXVSHknngx-*5

    cgxx

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    28/99

    Vkxsg jnvwt kxbw`gnts knd dgijng tzvgsjnt `kjn-jnt kxbc, cmkx /kxbyUP*

    u

    ji -kxbc+09* u

    wskbg-*5

    g}jt-;*5

    p

    jstxgk` /js 0 )cjn5

    jistxgk` jnijlg5

    ji -+stxcksgc`v-kxbyU;P,(stdjn(** u

    p glsg u

    jnijlg.avgn-kxbyU;P*5

    ji -+jnijlg* u

    cgxx

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    29/99

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    30/99

    Vxadwcg tmg awtvwtiax -wnsjbngd j065 j

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    31/99

    VgxjadjcSk`vlgdXgsawxcgSjbnkl

    Ts

    IaxrkxdRkyglgtStkbg

    Ta jnvwt aiIaxrkxdRkyglgtStkbgIaxrkxdRkyglgt

    Stkbg

    IaxrkxdRkyglgtStkbg

    IaxrkxdRkyglgtTxknsiax` -Stktjc ax Dznk`jc*

    largstQawtlyl

    largstQawtlyl % ;

    largstQawtlyl % nw`stkbgs ;

    largstQawtlyl % nw`stkbgs

    XgygxsgRkyglgtStkbg

    XgygxsgRkyglgtStkbg XgygxsgRkyglgt

    Stkbg

    Ta lar ixg{wgncz jnvwtai XgygxsgRkyglgtStkbg

    XgygxsgRkyglgtTxknsiax` -Stktjc ax Dznk`jc*

    IJXIjltgx-LVI*

    DarnSk`vlg

    IJXIjltgx-MVI*

    DarnSk`vlg

    Rkyglgt cagiijcjgnts Dglkzljng

    Darn sk`vlg xktg

    IJXIjltgx-LVI*

    WvSk`vlg

    Wv

    Sk`vlgIJXIjltgx

    -MVI*

    %

    Wv sk`vlg xktg Rkyglgt cagiijcjgnts Dglkzljng

    ]UnP

    Dglkz Hlace-Avtjankl*

    Vkxk`gtgxjgd hztmg

    nw`hgx ai lgyglsknd tmgdglkz yklwgs

    -wsgd iax kdowstjnb iax VX*

    OjttgxVxatgct@wltjStxgk`-Avtjankl*

    OjttgxVxatgctStxgk`

    -Avtjankl*

    Gssgntjkllz cansjstsai k

    OjttgxVxatgctStxgk`iaxgkcmjnca`jnb lgyglkndmks k hkcelab tmxgsmald

    iax gkcm lgygl

    Vkxk`gtgxjgd hz khkcelab tmxgsmad

    tmkt ancg g}cggdgd

    jndjcktgskctjan`wst hg tkegn

    Ijbwxg ;2? Szstg` saitrkxg dgsjbn.

    Sk`vlg

    SK@VLGTZVG Yklwg5 wnsjbngd jndg}5

    JnvwtSk`vlg AwtvwtSk`vlg

    RkyglgtJnvwtSk`vlg RkyglgtAwtvwtSk`vlg

    jnt lgygl5

    Ijbwxg ;=? Tmg sk`vlg clkss mjgxkxcmz.

    K ljstjnb ai tmg clkss jntgxikcgs rjtm k dgscxjvtjan ai tmg `g`hgx iwnctjans tmkt gkcm vxayjdg jsjn Kvvgndj} K.

    9.; Bgngxjc dgsjbn stkxtjnb rjtm sk`vlgs

    Jn axdgx ta kllar tmg dgsjbn ta hg bgngxkl iax `knz tzvgs ai wsgxs knd ca``wnjtjgs, tmg taalejt js

    hwjlt wsjnb tmg C%% bgngxjc clkss `gcmknjs s knd jnmgxjtkncg. Jn Ijbwxg ;= rg smar tmg sk`vlg

    clkss mjgxkxcmz. Kt tmg largst lgygl ai tmg taalejt tmgxg js tmg Sk`vlg hksg clkss tmkt js bgngxjckllz

    tzvgd hz k sk`vlg tzvg. Tmjs clkss vxayjdgs `knz avgxktaxs ta `knjvwlktg sk`vlgs, swcm ks kddjnb

    tra sk`vlgs tabgtmgx, sgttjnb tmg yklwgs ai tmg sk`vlg, knd bgttjnb tmg yklwg ai k sk`vlg. Tmg dktk

    kttxjhwtgs ai tmjs clkss jnclwdg tmg sk`vlg yklwg, knd tmg sk`vlg jndg}. Tmg sk`vlg jndg} kssw`gstmkt gkcm sk`vlg js g{wkllz svkcgd kvkxt. Tzvjckllz awtvwt sk`vlgs kxg xgsk`vlgd ta k largx sk`vlg

    xktg tmkn tmkt ai tmg jnvwt sk`vlg xktg jn axdgx ta xgdwcg xgdwndkncz jn tmg xgvxgsgntktjan. Tmjs

    rks djscwssgd jn `axg dgtkjl jn Sgctjan 3.

    Jnmgxjtgd ixa` tmg Sk`vlg hksg clkss, kxg tra clkssgs ckllgd JnvwtSk`vlg knd AwtvwtSk`vlg.

    Jn `ast sjtwktjans, rmgn vgxiax`jnb rkyglgt txknsiax` avgxktjans tmg jnvwt sk`vlgs knd awtvwt

    sk`vlgs kxg knnatktgd djiigxgntlz. Iax jnstkncg, tmg awtvwt sk`vlgs ai k rkyglgt txknsiax mkyg

    sa`g natjan ai lgygl ai tmg dgca`vasjtjan wnlgss tmg lgygl js gncadgd jn tmg hlace axdgxjnb ai tmg

    8:

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    32/99

    Sk`vlgHlace

    dg{wg sk`vlgs5 wnsjbngd hlacejndg}5

    JnvwtSk`vlgHlace AwtvwtSk`vlgHlace

    RkyglgtJnvwtSk`vlgHlace RkyglgtAwtvwtSk`vlgHlace

    jnt hlaceQlgygl5

    Ijbwxg ;:? Tmg sk`vlg hlace clkss mjgxkxcmz.

    sk`vlgs. Tmg jnvwt knd awtvwt sk`vlg clkssgs sgxyg ks tmg svljt hgtrggn tmg tra tzvgs ai sk`vlgs.

    Ang lgygl darn jn tmg mjgxkxcmz, kxg tmg clkssgs RkyglgtJnvwtSk`vlg knd RkyglgtAwtvwtSk`

    vlg. Tmg RkyglgtJnvwtSk`vlg clkss js swhclkssgd ixa` JnvwtSk`vlg. Jn awxkvvljcktjans, tmg SK@VLGTZVG js ai tzvg dawhlg. Tmg RkyglgtAwtvwtSk`vlg clkss js k swh

    clkss aiAwtvwtSk`vlg rmgxg tmg SK@VLGTZVG js klsa ai tzvg dawhlg. Tmgawtvwt sk`vlgs mkyg tmg kddjtjankl lgygl knnatktjan. Tmg lgygl ai tmg awtvwt sk`vlg js sgt ancg

    rkyglgt txknsiax`ktjans kxg vgxia`xgd, knd js `gknjnblgss wntjl tmgn. Tmg lgygl ai tmg awtvwt sk`

    vlg js kssjbngd stkxtjnb rjtm tmg mjbmgst ixg{wgncz hknd dgsjbnktgd hz largst awtlyl, k vkxk`gtgx

    ai tmg txknsiax` avgxktjan. Tmg lgygl nw`hgx jncxgksgs ks tmg sk`vlg xgvxgsgnts largx ixg{wgncz

    jniax`ktjan. Tmjs js g}vljcjtlz smarn jn Ijbwxg ;2.

    Ji k wsgx rawld ljeg ta cxgktg tmgjx arn sk`vlg tzvg, tmjs js dang hz swhclkssjnb ixa` tmg

    JnvwtSk`vlg knd AwtvwtSk`vlg clkssgs.

    9.8 Kbbxgbktjnb sk`vlgs jnta hlacesSjncg ang ai tmg xg{wjxg`gnts ai tmg taalejt js ta vgxiax` hlace avgxktjans an kbbxgbktgd sk`vlgs,

    rg mkyg cxgktgd tmg Sk`vlgHlace dktk tzvg knd jts swhclkssgs. Tmjs js smarn jn Ijbwxg ;:.

    Tmg Sk`vlgHlace clkss sgxygs ks tmg hksg clkss ai tmg hlace dktktzvgs. Jn tmg tzvjckl sgnsg

    hwt nat xgstxjctgd ta, tmg Sk`vlgHlace clkss js tzvgd hz awx Sk`vlg clkss djscwssgd vxgyjawslz.

    Jt wsgs tmg C%% Stkndkxd Tg`vlktg Ljhxkxz -STL* dg{wg cantkjngx clkss iax kbbxgbktjnb hlaces

    ai sk`vlgs. Tmg xgksan iax wsjnb tmg dg{wg dktk stxwctwxg, js dwg ta tmg ikct tmkt sa`g ai tmg

    txknsiax`ktjans knd klbaxjtm`s j`vlg`gntgd jn tmg taalejt cantkjn dktk kccgss vkttgxns tmkt kdd

    sk`vlgs ta tmg hgbjnnjnb knd ta tmg gnd. Tmg atmgx dktk `g`hgx ai tmg Sk`vlgHlace clkss js tmg

    hlace jndg}. Gygn tmawbm sk`vlgs ks xgvxgsgntgd hz tmg Sk`vlg clkss cantkjn k dktk `g`hgx iax

    jndg}jnb, jt js `wcm `axg gicjgnt rmgn raxejnb rjtm sk`vlg hlaces ta mkyg k hlace jndg} jnstgkdai mkyjnb ta vggx jn kt tmg sk`vlgs djxgctlz. Tmgxg js kn wndgxlzjnb kssw`vtjan ta wsjnb sk`vlg

    hlaces, knd tmkt js tmkt gkcm ai tmg sk`vlgs cantkjngd rjtmjn tmg hlace kxg jn axdgx knd tmgxg kxg na

    `jssjnb sk`vlgs rjtmjn tmg hlace.

    Tmg Sk`vlgHlace clkss vxayjdgs `knz jntgxikcgs iax raxejnb rjtm hlaces ai sk`vlgs. Tmgsg

    jnclwdg `g`hgx iwnctjans iax ahtkjnjnb svgcjc sk`vlgs, ahtkjnjnb k swhsgt ai tmg sk`vlgs, vwsm

    jnb knd vavvjnb sk`vlgs jnta knd awt ai tmg hlace, knd kddjnb tra hlaces tabgtmgx. Tmgsg khstxkc

    tjans `keg jt gksz ta raxe rjtm hlaces jn tmg cantg}t ai ltgxjnb, xgsk`vljnb knd txknsiax`jnb

    36

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    33/99

    OjttgxVxatgctStxgk

    OjttgxVxatgct@wltjStxgk`

    wn sjbngd hkcelabQtmxgsmald5 wnsjbngd cwxxgntQjndg}5 ljst ojttgxQhwiigx5

    wnsjbngd nw`lgygls5

    wn sjbngd /hkcelabs5

    ;

    nw`hgxQaiQstxgk`s

    Ijbwxg 86? Tmg ojttgx vxatgctjan clkssgs.

    hlaces jnta tmg rkyglgt da`kjn.

    Tmg stxwctwxg ai tmg Sk`vlgHlace mjgxkxcmz iallars sj`jlkxlz ta tmkt ai tmg Sk`vlg clkss mjgx

    kxcmz. Tmgxg kxg tra swhclkssgs ai Sk`vlgHlace. Tmgsg kxg tmg JnvwtSk`vlgHlace knd tmg Awt

    vwtSk`vlgHlace. Swhclkssgd ixa` tmgsg kxg tmg RkyglgtJnvwtSk`vlgHlace knd tmg RkyglgtAwtvwtSk`vlgHlace. Tmg RkyglgtJnvwtSk`vlgHlace js kn JnvwtSk`vlgHlace, hwt vkxk`gtgxjgd hz

    tmg sk`vlg clkss RkyglgtJnvwtSk`vlg. Tmg RkyglgtAwtvwtSk`vlgHlace js kn AwtvwtSk`vlgHlace, hwt jt cantkjns tmg g}txk kttxjhwtg ta dgsjbnktg tmg lgygl ai tmg dgca`vasjtjan tmg

    hlace ai sk`vlgs xgvxgsgnt.

    Ljeg tmg sk`vlg clkssgs, ji ang rknts ta `keg k djiigxgnt sk`vlghlace tzvg iax k djiigxgnt

    vwxvasg tmkn awx svgcjc vwxvasg, tmgz `kz sj`vlz swhclkss aii ai JnvwtSk`vlgHlace knd Awt

    vwtSk`vlgHlace ta kddxgss tmgjx vkxtjcwlkx nggds. Rg hgljgyg tmkt tmg sk`vlg knd sk`vlg hlace

    stxwctwxg tmkt rg mkyg cxgktgd js bgngxjc ta tmg g}tgnt tmkt knz tzvg ai sk`vlg iax knz tzvg ai

    vwxvasg ckn hg cxgktgd rjtmjn tmg ixk`graxe tmkt rg vxayjdg.

    Kn g}k`vlg ai mar ta raxe rjtm tmgsg clkssgs ks xglktgd ta awx ca``wnjtz ai knklzjnb xg

    sawxcg sjbnkl sk`vlgs jn djstxjhwtgd ca`vwtjnb js smarn ks iallars

    !! Cxgktg k tzvg dgijnjtjan iax jnvwt knd awtvwt sk`vlgs

    tzvgdgi RkyglgtJnvwtSk`vlg rjsd5

    tzvgdgi RkyglgtAwtvwtSk`vlg rasd5

    !!Cxgktg sa`g jnvwt knd awtvwt hlaces ai sk`vlgs

    RkyglgtJnvwtSk`vlgHlace jnvwthlace5

    RkyglgtAwtvwtSk`vlgHlace awtvwthlace5

    Ancg tmg rjsd knd rasd tzvgs mkyg hggn cxgktgd, jt js ygxz gksz ta tzvg atmgx avgxktjans tmkt rg

    rjll djscwss jn tmg iallarjnb clkss dgscxjvtjans.

    9.3 Ojttgx vxatgctjan

    Hgckwsg Tswnk`j js k szstg` hwjlt iax wsg jn djstxjhwtgd ca`vwtjnb knd hgckwsg, jn tmjs da`kjn,

    sk`vlgs kxg tzvjckllz sgnt aygx kn wnxgljkhlg ngtraxe, tmg szstg` `wst kvvxavxjktglz dgkl rjtm

    lass, caxxwvtjan knd sk`vlgs kxxjyjnb lktg. Jn axdgx ta dgkl rjtm tmgsg vxahlg`s, Tswnk`j vxayjdgs

    ojttgx ca`vangnts iax mkndljnb kll ai tmgsg cksgs.

    3;

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    34/99

    _gxaIjllKctjan

    wnsjbngd OjttgxKctjan-ljst )sk`vlgs,canst wnsjbngd cwxxgntQjnd}*

    JntgxvalktgIjllKctjan

    wnsjbngd OjttgxKctjan-ljst )sk`vlgs,

    canst wnsjbngd cwxxgntQjnd}*

    Ijbwxg 8;? Tmg ojttgx kctjan clkssgs.

    Ji Tswnk`j js wsgd rjtm TCV, caxxwvtjan knd lass js dgklt rjtm kvvxavxjktglz jn tmg TCV vxatacal

    stkce. Margygx, tmg sk`vlg kxxjykl tj`gs kxg nat bwkxkntggd jn TCV knd tmgxgiaxg tmg szstg` `wst

    dgkl rjtm tmg sk`vlgs tmkt kxxjyg lktg. Tmg ykxzjnb kxxjykl tj`gs ai sk`vlgs js enarn ks ojttgx. Jn

    kddjtjan, ji wsgd rjtm WDV, tmgxg js na bwkxkntgg tmkt sk`vlgs rjll kxxjyg kt kll, knd tmg szstg` rjll

    nggd ta dgkl rjtm last sk`vlgs klsa. Ta dgkl rjtm tmgsg tzvgs ai xgljkhjljtz vxahlg s, tmg taalejt

    vxayjdgs k sgt ai clkssgs ta mkndlg ojttgx knd lass jn tmg ngtraxe jn tmg kvvxavxjktg `knngx.

    Tmg ojttgx vxatgctjan clkssgs tmkt rg vxayjdg kxg smarn jn Ijbwxg 86. Tmg clkss OjttgxVxa

    tgctStxgk` ckn vxatgct stxgk`s ai sk`vlgs ax stxgk`s ai hlaces hgjnb sgnt aygx tmg ngtraxe iax

    vxacgssjnb. Tmjs js tzvjckllz tmg cksg rmgn tmg `kcmjng xwnnjnb tmg sgnsax sj`vlz callgcts `gk

    swxg`gnts knd sgnds tmg` aii ta knatmgx `kcmjng iax ca`vwtjnb tmg txknsiax`ktjans. Tmjs clkss

    cantkjns k ojttgx hwiigx iax xgaxdgxjnb tmg sk`vlgs, kn jndg} ai tmg sk`vlg tmkt js ng}t g}vgctgd

    ixa` tmg ngtraxe, knd k hkcelab tmxgsmald tmkt dgtgx`jngs rmgn ta tkeg tmg kvvxavxjktg kctjan iax

    }jnb tmg ojttgx vxahlg`. Tmg clkss OjttgxVxatgct@wltjStxgk` vxatgcts `wltjvlg stxgk`s ai sk`vlgs

    hz wsjnb lgygl jniax`ktjan knd sk`vlg ax hlace jndjcgs. Tmjs clkss sj`vlz wsgs tmg clkss OjttgxVxa

    tgctStxgk` iax gkcm ai jts `wltjvlg stxgk s. Tmg OjttgxVxatgct@wltjStxgk` mks kn kxxkz ai hkcelabtmxgsmalds iax gkcm stxgk` tmkt jt js vxatgctjnb. Rmgn k vkxtjcwlkx tmxgsmald mks hggn g}cggdgd,

    `jssjnb sk`vlgs `wst hg llgd kvvxavxjktglz hgiaxg vxacgssjnb ckn cantjnwg. Hgckwsg tmgxg js k

    natjan ai vgxigct xgcanstxwctjan jn rkyglgt knklzsjs, ojttgx xgcaygxz js j`vaxtknt iax xgdwcjnb tmg

    gxxax hgtrggn tmg jnvwt xgsawxcg sjbnkl knd tmg xgcanstxwctgd sjbnkl.

    Rmgn gjtmgx ai tmgsg ca`vangnts sgnsg ojttgx knd ax kn g}txg`g lass ai sk`vlgs, tmg ojttgx kctjan

    xawtjngs kxg ckllgd jn axdgx ta eggv tmg szstg` `ayjnb iaxrkxd. Tmg ojttgx kctjan clkssgs kxg smarn

    jn Ijbwxg 8;. Tmg xst kctjan clkss, _gxaIjllKctjan, gxa lls `jssjnb sk`vlgs sa tmkt tmg szstg`

    ckn vxabxgss. Tmg sgcand kctjan clkss, JntgxvalktgIjllKctjan, rjll ll jn sk`vlgs kccaxdjnb ta kn

    kygxkbg aygx tmg sk`vlgs xgcgjygd tmws ikx. Wsgxs ckn g}tgnd tmg taalejt hz kddjnb atmgx ojttgx kctjan

    clkssgs hz vkxk`gtgxjjnb OjttgxVxatgctStxgk` knd OjttgxVxatgct@wltjStxgk` hz k ojttgx kctjan clkss.

    Gkcm ngr ojttgx kctjan clkss tmkt js hwjlt, rjll cxgktg k OjttgxKctjan `g`hgx iwnctjan tmkt tkegs kskxbw`gnts tmg cwxxgnt jndg} knd kn STL ljst dktk stxwctwxg iax tmg ngrlz cxgktgd awtvwt sk`vlgs.

    Ks kn g}k`vlg, ta vxatgct RkyglgtJnvwtSk`vlgs ixa` ojttgx ks tmgz kxg smjvvgd ta knatmgx `kcmjng

    iax txknsiax`ktjan vxacgssjnb, knd wsjnb tmg _gxaIjllKctjan clkss iax sk`vlg xgcaygxz, ang rawld

    jnstkntjktg k stxgk` hz tmg iallarjnb?

    !! Jnstkntjktg k ojttgx vxatgctjan clkss an k

    !! RkyglgtJnvwtSk`vlg stxgk` wsjnb _gxaIjllKctjan

    38

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    35/99

    IJXIjltgx

    ygctax cagiijcjgnts5

    dg{wg/ dglkzljng5 wnsjbngd nw`hgxQaiQcagis5 BgtI jltgxAwtvwt-Sk`vlg )awt,

    Sk`vlg )jn*5

    BgtIjltgxHwiigxAwtvwt-Sk`vlgHlace )awt,Sk`vlgHlace )jn*5

    Ijbwxg 88? Tmg IJX ltgx clkss.

    WvSk`vlg

    DarnSk`vlg

    wnsjbngd xktg5 wnsjbngd sk`vlgcawnt5 haal _gxaSk`vlg-*5 yajd WvSk`vlgHwiigx-Sk`vlgHlace )awt,

    Sk`vlgHlace )jn*5

    wnsjbngd xktg5 wnsjbngd sk`vlgcawnt5 haal EggvSk`vlg-*5 yajd DarnSk`vlgHwiigx-Sk vlgHlace )awt,

    Sk`vlgHlace )jn*5

    Ijbwxg 83? Tmg wv knd darn sk`vlg clkssgs.

    tzvgdgi RkyglgtJnvwtSk`vlg rjsd5

    OjttgxVxatgctStxgk` ovs5

    Kltmawbm ojttgx vxatgctjan js k `wcm hjbbgx xg{wjxg`gnt iax Tswnk`j tmkn iax XVS, tmjs sgt ai

    clkssgs ckn hg wsgd iax ojttgx vxatgctjan iax stkndkxd XVS ca``wnjcktjan ks rgll.

    9.4 Ijng-bxkjn hwjldjnb hlaces

    Ta kddxgss tmg bakl ai ngbxkjn hwjldjnb hlaces, rg cmasg ta svljt wv gkcm ai tmg vxacgssjnb ca`vangnts jnta ngbxkjngd `adwlgs sa tmkt `knz djiigxgnt tzvgs ai stxwctwxgs ckn hg canstxwctgd.

    Tmg ahogcts tmkt rg djscwss ng}t kxg smarn jn tmg sj`vlg trahknd ltgx hkne g}k`vlg jn Ijb

    wxg 7-h*. Jn axdgx ta cxgktg tmg stxwctwxg smarn jn tmg bwxg, rg nggd ta j`vlg`gnt ltgxs ai

    ykxjaws cmkxkctgxjstjcs jnclwdjnb larvkss knd hkndvkss xgsvansgs, dgcj`ktaxs knd g}vkndgxs. Jn

    tmjs xgvaxt, rg wsg dgcj`ktaxs knd darnsk`vlgxs, knd g}vkndgxs knd wvsk`vlgxs jntgxcmknbgkhlz.

    Jn Ijbwxg 88, rg smar kn IJX ltgx j`vlg`gntktjan vkxk`gtgxjgd hz tmg sk`vlg tzvgs can

    tkjngd jn tmg dglkz ljng ai tmg ltgx, knd tmg jnvwt knd awtvwt sk`vlg tzvgs ai tmg avgxktjan. Kt

    33

  • 8/6/2019 Tech Report NWU-CS-03-16: Tsunami: A Wavelet Toolkit for Distributed Systems

    36/99

    txjhwtgs ai tmg IJX ltgx jnclwdg tmg cagicjgnts tmkt cmkxkctgxjg tmg ltgx, tmg dglkz ljng ai tmg

    ltgx, knd tmg nw`hgx ai cagicjgnts wsgd jn tmg vkxtjcwlkx ltgx. Sjncg tmg szstg` js hksgd an

    rkyglgts knd rg mkyg anlz j`vlg`gntgd tmg Dkwhgcmjgs dgsjbngd ltgxs U4P, rg cwxxgntlz anlz

    mkyg swvvaxt iax IJX ltgxs. Tmg ltgx clkss ckn hg wsgd jn sk`vlg avgxktjan ax hlace avgxktjan,

    iallarjnb tmg aygxkll bakl ai `wltjvljcjtz jn avgxktjan.

    Jn Ijbwxg 83, rg smar tmg wv knd darn sk`vljnb clkssgs. Tmg dgcj`ktax sgctjan ai tmg stxwctwxgjs j`vlg`gntgd jn tmg DarnSk`vlg clkss knd js vkxk`gtgxjgd hz tmg tzvg ai sk`vlg tmkt rjll hg

    jnvwt knd lktgx awtvwt. Tmg kssw`vtjan rjtm tmg DarnSk`vlg clkss, js tmkt rmktgygx sk`vlg tzvg

    js jnvwt rjll klsa hg awtvwt. Tmg darn sk`vlg avgxktjan ckn hg xwn kt knz darn sk`vlg xktg rmjcm

    js tzvjckllz k iwnctjan ai tmg tzvg ai dgca`vasjtjan. Jn tmg trahknd stxwctwxg smarn jn tmg bwxg,

    rg darn sk`vlg hz tra. Tmg avgxktjan ckn hg xwn an sk`vlgs hz wsjnb tmg `g`hgx iwnctjan

    EggvSk`vlg-* ax jn hlace `adg rjtm tmg iwnctjan DarnSk`vlgHwiigx-*.

    Tmg g}vkndgx sgctjan js j`vlg`gntgd jn tmg WvSk`vlg clkss knd js vkxk`gtgxjgd hz tmg tzvg

    ai sk`vlg, sj`jlkx ta tmg DarnSk`vlg clkss. Jt cantkjns tmg sk`g kssw`vtjans xglktgd ta tmg

    vkxk`gtgxjktjan ai jnvwt knd awtvwt sk`vlgs ks tmg DarnSk`vlg clkss. Tmg wv sk`vlg clkss

    ckn hg xwn kt knz xktg knd js klsa k iwnctjan ai tmg tzvg ai stxwctwxg. Jn tmg trahknd bwxg

    dgca`vasjtjan, tmg wv sk`vlg xktg js tra. Sj`jlkxlz ta tmg DarnSk`vlgclkss, tmg WvSk`vlgclkss

    ckn hg xwn an sk`vlgs ax an hlaces ai sk`vlgs.

    9.7 Swvvaxt iax `knz ltgxs

    Jn axdgx ta swvvaxt tmg bakl ai g}tgnsjhjljtz jn ltgxjnb, rg rawld ljeg ta swvvaxt `knz djiigxgnt

    tzvgs ai