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References Ci ted

U . S . PATENT DOCUMENTS

6,618,725 B1* 9 / 2003 Fukuda t a 1 . . . . . . . . . . . . . . . . . . ... 7 0 7 / 66 , 8 0 4 , 6 6 4B 1 * 1 0 / 2 0 0 4 H a r t m a n t a 1 . 1 / 17 , 5 4 8 , 9 2 8 B1 6/2009 Dean t a 1 . . . . . . . . .. . . 1/1

7 , 6 3 0 , 9 9 6 B1 1 2 / 2 0 0 9 H e r s h k o v i c h e t a l . . . . . . . . . . . . . . .. . l / l

2004/0024790 A1 * 2/2004 E v e r e t t . . . . . . . 707/200

2006/0106797 A1 * 5 / 2 0 0 6 Sr in ivasa e t a l . . . . . . . . . . . . . . . . ... 7 0 7 / 6

OTHER PUBLICATIONS

A g r a W a l ,R . a n d R . S r i k a n t . F a s tA l g o r i t h m sf o rM i n i n gA s s o c i a t i o nR u l e s . P r o c e e d i n g s o ft h e 2 0 t h VLDB o n f e r e n c e , p p . 4 8 7 - 4 9 9 .S a n t i a g o , C h i l e , l 9 9 4 .Ay r e s , J a y e t a l . S e q u e n t i a lP a t t e r nM i n i n g U s i n ga B i t m a pR e p r es e n t a t i o n . P r o c e e d i n g s o ft h e 8 t h ACM I G K D D n t l .C o n f e r e n c e ,p p . 4 2 9 - 4 3 5 .ACM r e s s , NeWYork, NY, 2 0 0 2 .Y i n - F u Huang e t a l : M i n i n gg e n e r a l i z e da s s o c i a t i o n r u l e su s i n gp r u n i n gt e c h n i q u e s D a t a M i n i n g , 2 0 0 2 . P r o c ee d i ng s .2 0 0 2IEEEI n t e r n a t i o n a l C o n f e r e n c eo n M a e b a s h iC i t y ,J a p a n D e c .9 - 1 2 , 2 0 0 2 ,L o s A l a m i t o s ,CA, USA,IEEE C o m p u t .S o c . U S , D e c . 9 , 2 0 0 2 ,p p .2 2 7 - 2 3 4 ,X P 0 1 0 8 0 5 1 2 0 ISBN: 0 - 7 6 9 5 - 1 7 5 4 - 4 .

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OTHER PUBLICATIONS

P r a d e e p S h e n o ye t a l . : T u r b o - c h a r g i n gv e r t i c a lm i n i n g o f l a r g ed a t a b a s e s P r o c e e d i n g so f t h e 2000 ACM SIGMOD n t e r n a t i o n a lC o n f e r e n c eon M a n agemen t f D a t a , 2 0 0 0 ,p p . 2 2 - 3 3 ,XP00243 5 0 7D a l l a s Te x a s , U n i t e dS t a t e s .S r i k a n tR t a 1 : M i n i n gG e n e r a l i z e dA s s o c i a t i o nR u l e s P r o c e e d i n g so f t h e I n t e r n a t i o n a l C o n f e r e n c eo n Ve r yL a r g e D a t aB a s e s , S e p . 1 1 ,1 9 9 5 , p p .4 0 7 - 4 1 9 ,XP000671664.M o h a m m e d . Z a k i e t a l . : F a s t v e r t i c a l m i n i n gu s i n g d i f f s e t s P r oc e e d i n g s o ft h e N i n t hACM SIGKDD n t e r n a t i o n a l Conference on

K n o w l e d g eD i s c o v e r y a n d D a t a M i n i n g , 2 0 0 3 ,p p . 3 2 6 - 3 3 5 ,XP002431508 Wa s h i n g t o n ,DC, S .P C T i I n t e r n a t i o n a lS e a r c h i n gA u t h o r i t y : I n v i t a t i o n t o pay a d d it i o n a lf e e s c o m m u n i c a t i o ni n c o u n t e r p a r t P C T a p p l i c a t i o n PCT/E P 2 0 0 7 / 0 5 l 0 2 5 ,May 5 , 2 0 0 7 .

P C T i I n t e r n a t i o n a lS e a r c hR e p o r ta n d The W r i t t e n O p i n i o n o ft h eI n t e r n a t i o n a lS e a r c h A u t h o r i t y . PCT a p p l i c a t i o n :P C T / E P 2 0 0 7 /0 5 1 0 2 5 .Mailed N o v . 1 4 ,2 0 0 7 .

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all N bits set to l;

I 0;

w h i l e ( i t e m P o s i i g < g.numberOfDifferentltems ){

i f ( q . i t e m l D [ i t e m P o s i _q ] < i t e m l D s [ i t e m P o s i ]{

itemPosi_q :2 itemPosi_g + l ;

}e l s e i f ( g . i t e m I D [ i t e m P o s i _g ] > i t e m l D s [ i t e m P o s i ]

}return 0 ;

else

{activeTAs : = activeTAs & g.bitField[itemPosiig]

itemPosi_g : = itemPosi_g + l ;

itemPosi : : itemPosi + 1 ;i f (itemPosi = numberOfltems) return activeTAs;

return 0 ;

F I G . 10B

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US. P a t e n t A u g .2 1 ,2 0 1 2 S h e e t1 4 0 f 2 2 US , 2 5 0 , 1 0 5B 2

(150) i n l i n e i n t c o u n t l B i t s ( u n s i g n e d l o n g l o n g b i t F i e l d

= (unsigned char*) (&bitField)

n b l B i t s [(152) u n s i g n e d char* p( 1 5 3 ) i n t nbItems

( 1 5 4 )1 ;

]]

nbIterrs +: nblBits

nbItems += nblBits

nbIterns += nblBits

nbIterns += nblBits

nbIterts += nblBits

nbIterrs += nblBits

nbItenis += nblBits

return n b I t e m s ;1 5 6 )

(160) c o n s t unsigned c h a r n b l B i t s [ 2 5 6 ]

I

2 223I3

F I G . 10C

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12001 2 0 1

/ /s t a r tw i t h c a n d i d a t e l i s t l ,c o n t a i n i n g N r u l ec a n d i d a t e s

w i t h k i t e m s , 1 1 - 1o f them i d e n t i c a l f o r a l l c a n d i d a t e s

1002a,\/ ,

1003 l . h a s P a r e n t . 1004\ \ i f 11 I1

f e t c h f i r s tTA e t 9 f e t c h p a r e n t s f i r s ta c t i v e T A s e t 9

no / y e s. n b D | f f | t e n | s < k

1 2 0 2 1 0 0 5a c t i v e TA s: = f i n d A c t i v e TA s ig , k - 1 i d e n t i c a li t e m s )

n o HIE e s1 2 0 4 < I a \ c 1 1 v e TA se m\ I 2 0 3i : = 0 ; i temPosi : = 0

1 1 1 2 0 5/_/

A . 1 2W 8 5 s

[ I 2 0 6A a c t i v e TA s _ i: : a c t i v e TA s& f i n d A c t i v e TA s (g , a d d e d i t e m ? ] ,i t e r h P o s i)ia b s S u p p o r t [i ] : : a b s S u p p o r t [i ] + c o u n t 1 B i t s (a c t i v e TA s _ i // 2 0 7

ii : = i + 1 / / 1 2 O 8

1 0 0 8 ain o >/\ e s1 ?

1009 1010\ \ 1 1 1 1 /

f e t c h n e x t TA e t 9 f e t c h p a r e n t s n e x t a c t i v e TA e t g

? / w / t i b y g , Y E Sf i n i s h e d 1 0 1 1

F I G . 1 2 A

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U S . P a t e n t

B I T F I E L D _ N f i n d A C t i Ve TA S (

A u g .2 1 ,2 0 1 2 S h e e t 1 70 f 2 2 US , 2 5 0 , 1 0 5B 2

TAGROUP g , ITEMH i t e m l D s , I T E MnumberOfltems

BITFIELD_N activeTAs : 2ITEM itemPosi_g I 0 ;

ITEM itemPosi : 2 0;

w h i l e ( i t e m P o s i _ g < g.numberOfDifferentltems ) ){

i f

{

all N bits set to l;

( g . i t e m l D [ i t e m P 0 s i _ g ] < i t e m l D s [ i t e m P o s i ] )

itemPosi_g : 2 itemPosi_g + l ;

else i f{

( g . i t e m I D [ i t e m P o s i _ g ] > i t e m l D s [ i t e m P o s i ] )

return 0 ;

else

{activeTAs : = activeTAs & g.bitField[itemPosi_g]

itemPosi_g :2 itemPosi_g + l ;

itemPosi : 2 itemPosi + 1;

if (itemPosi I numberOfltems) return activeTAs;

return 0 ;

F I G . 12B

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BITFIELD_N findACtiVeTAS( TAGROUP g , ITEMID i t e m I D , i n t &i t e m P o s i

{w h i l e ( i t e m P o s i < g.numberOfDifferentItems(){

i f (g.itemID[itemPosi] < i t e m I D ){

itemPosi : 2 itemPosi + l ;

}i f ( g . i t e m I D [ i t e m P o s i ] > i t e m I D ) {

itemPosi : 2 g.numberOfDifferentItems()

1

e l s e {return g.bitField[itemPosi]

return 0 ;

F I G . 12C

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