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INDEX

Achi~veinent of the Steincr ratio. 78

Acyclic. 13 Adjacency matris . 37 Adjacent, 12 ;Ilgorit,hrn. 59

~loildetcr~riiriist,iq 66 Align~nerit,, 141

induced. 132 local, 149 rriultiple, 130 optimal, 148 pairn-ise. 141

Alphabet. 132 binary, 132 cxtelided, 151

Xricestor. 183 immediate. 185

=Ipprosirnable. 75 Approxirriation. 74 Arc, 183 ahyrnptotic behavior. 175 -irerage-case perforniaric~, 63 Ball, 10. 37. 195 Ball family. 196 Banach-SIiiikon-ski space. 40 Baliach-TT'iener space. 40 Banach space, 40 Base pairs, 131 Bell~nan's principle. 47 Binary matrix, 37 Binary LIST: 117 Binary search. G3 Binary tree. 13. 180

Bipartite, 53 Bisector. 71 Boolean matris . 37 Borur-la's algorithm, 16 Bounded Degree 51inimuni

Sparirii~ig Tree, 117 ge~ieralized, 118

Bounded set. 37 Bp. 131 Bracket fomiat. 181 Branch arid bound. 52 Bridgc, 14 C. dj ,l e~ .' s . tree formula, 179

Center: 10 Center function, 9 Center tree, 208 Central dogma. 209 Cent,ral Dogma of Slolecular

Biology: 91. 132 Chain. 13 Character-state matrix: 159 Character. 126. 138 Chinese Postnlari Probleni. 109 Chomsky hierarch!-. 134 Chrorriosonie. 131 Church's thesis. 60 Circlc: 10 Class. 193 Classes of complexity. 62 Classification. 162, 192 ~ 1 . awfication :. .' metric, 195 Cluster-distance, 218 Cluster. 193 Conmion ancestor. 164

last 11ni~-ersal. 164 most recent, 164

Con~patible splits. 182 Complete alignment, 153 Cornplet,e graph. 13 Cornpletc linkage clustering. 220 Component, 14 Computational cornplesity, 63 Concatenation. 133 Connected component, 14 Connected graph. 13 Connected

strongly, 185 Consens~is letter, 155 Consensus secluellce. 154 Consensus Sequeiic.e Problem. 155 Consensus trec., 227 Consensus

majority, 228 strict. 228

Construction x i th ruler and co1npass; 5

Content. 193 Come?: polytope. 87 Cook's hypothesis. 67 Cost measure. 138

generalized, 15 1 Counting problern. 174 Covering, 10 Cubic graph, 12 Cubic time, 62 Cycle. 12-13 Decomposition of a tree, 102 Degree, 12 Delaunay triangulation, 20. 71. 103 Dendrograni, 198 Depth of the tree. 186 Diameter. 201 Diameter of a graph. 49 Different and isomorphic. 175 Digraph, 185

Dijkstra's algorithm (rninirnum spanning tree). 68

Dijkstra's algorithm (shortest path). 47

Directed graph. 185 Dircction of an arc, 185 Discrct,e rnct,ric. 1 1 Discrete metric space. 41 Dissiniilarity. 32 Distance. 32 Distance graph: 46 Distancc matrix. 217 Distance t,ree, 37 Diversity, 128, 165 Di~.itie and Coriyuer rnetliocl, 229 DN.4. 131 Dominance region, 70 DT. 20, 71. 105 Dyna~nic progran~ming algorithm.

147 Dj.na~nic programming technique;

47 Edge. 12 Edit, clist,arice, 136 Elementary tree tra~~sformat~ion,

201 Ernbedcling of a graph in a metric

space. 32 Empt,y circle condition. 10; Empt,y IT-ord, 133 E n d v ~ r t e s , 12 Enurnc~at,ion problem. 174. 205 Error of an algorithm. 7.5 Euclidean metric. 42 Euclitlcan planc. 3. 42 Euler's formula; 53 Eulerian chain. 107 Eulerian c j d e , 107 Eulerian graph. 107 Farris' method. 213 Fer~nat ' s Problem. 2. 206 Fcrmat function. 3; 206

Index

generalized. 85 Forest,, 14 Full components, 102 Full t,ree, 25, 43 Fully polynomial approxi~nation

scheme, 75 Gap, 142 G a d question, 22 Generating graphs, 188 Generating trees, 189 Genome, 131 Geodesic curve: 42 Geometry of Sumhers, 202 Gill-mt-Pollnk conjectilre. 79 Graph, 11 Graph alignment. 132 Graph

regular, 12 Greedj. algorit,hm. 18 Greedy Tree, 84 GT. 84 Hadn-iger 11u1dxr. 94 Hamiltonian cycle. 108 Hatniltonian graph, 108 Hani~nirig-dist,arice

extended. 137 Harriinirig clist~ance, 135 Harriming n-eight, 203 Heuristic, 74 Hierarchy. 197 Hicrholzer's algorith~n. 108 Hilbert's fourth problem, 40 Homologous. 138 Hypercube. 13.5; 173 Incident, 12 Indegree, 185 Indel. 139 Internal edge. 184 Internal vertes, 14 Intractable, 66 Isornorphic. 174 Isoinorphisrn. 174

K-conected Steiner ratio. 116 K-connected. 114 K-edge-connected graph. 113 K-edge-connected llinirnuln

Spanning Net,work. 116 K-edge-connected St,eincr lZIinirna1

Network. 114 I<-edge-IISN, 116 Ksizr-Steiner ratio, 103 I<-size S I IT . 102 Ksize tree. 102 I<-SLIT, 93 I<-vertex-connectcd. 114 Kissing number, 94 I<rusltal's algorithm. 17 Kya, 168 Labelled graph, 175

partially, I75 Laliguage. 134 Last iu i i~wsa l coninion ancestor.

164, 187 Leaf, 14 Leiigt,h fun~ t~ ion . 16 Length of a graph in a ~net~r ic

space. 33 Length of a subgraph: 16 Leiigtli of a n-ord, 133 L c ~ e l . 186 Levenslitein distance, 136, 146 Lesicographic order. 134 Lincar order. 64 Linearly ordered set, 64 Linkage clustering. 220 Linnaeus' system, 161 Longest coinnion subsequence. 146 LUCA, 164 Lunc. 104 AIajority rule: 134, 207

restricted. 134 hIa111iatt~a11 Steirler Problem, 89 ;\Iat,ch-mismat,c2l-g.ap system, 146

normecl. 146

standaid. 146 hlatch. 142 hIatc hmg, 109 hIathematici. 36 hIatrix of admi t tmte , 199 Slaxinium Parsimonj. 128. 213 SIasimurn par simony pioblem 156 Slaximum Par sirnony Tree, 129 nrcc, l o AIDST. 120 AIedian. 9. 207 SIedian function 9 Slcdian tree, 208 \Iel~ali 's dlgor i t l m 23 SIetapln s ~ c . 35 S I e t r ~ . 32 hIetric closuie 46 hIe t11~ b p a c ~ . 31 IIetric ipace of all ipanning trees,

201 AIctric space of N-treei. 183 IIetric ipace of looted N-tlces. 195 Slillion J eals ago. 164 SIinimurn col cling cir t lc 10 hIinimurn D~anietci Spalining

Tree, 119 I\liriimum Perfect ;\latcliing

Problem 110 Slinimurn spanning t r cc 16 lliriimum spanning t iec pr ohlern.

11, 16 hIinlion ski functiol~al, 39 hl~srnatch. 142 Slitothor~drial E.\e 167 Slonotonic iterative dlgoritliin. 99 AIR. 154 S E T , 19 l I tEve. 167 SIultigr aph 107 AIultiplr alignment

optimdl, 152 hIultiple ~ o r l r l e c t ~ d graph 113

Slultiregional model, 167 AIya. 164 X-tree- 177

rooted. 178 Neighbor, 12 Set~vorli . 11: 16: 46 Nenick format, 181 Norm. 39 KP-complete: 66 NP-llard, 66 NP: 66 SPC'. 66 S P I : 67 Nunlbcr-P- corr~plcte, 206 N ~ m b e r of leaves in a tree, 15 Niimber of spanning trees, 199 Numbcr of splits. 182 S u ~ n b e r of words, 204 Ocltham's razor. 129. 213 Optimal algorithm. 63 Oracle. 68 Order notations. 62 Order of growing. 61, 175 Out of Africa moclel: 167 Outdegree. 185 P-norm. 85 P. 65 Pair group inet,hod. 198. 217 Partial order; 64 Partiallj- ordered set; 64 Pat,h. 13: 13 Pat,lls

illdependent. 113 Perfert matching, 12. 109 Perfect phylogeny. 159 Perfect pl~ylogeny problem, 139 Perfect phylogeny problem, 215 PGAI. 198, 217 Phylogenetic space, 136 Phylogenetic tree. 123 Phylogenetic Tree Problem. 127 Phyloger~y, 123 1 2 4

Planar, 33 Planar code; 191 Polyhedral approach. 31 Polynornial algorithm. 63 Polynomially hounded, 63 Poset; 64 Priifer's decoding, 190 Priifer's encoding. 189 Priifer code, 189 Prim's algorit,lirn, 68 Problclri of Classification. 162 Problem of lriiriirnal covering. 10 Problem of AIST. 19 Protein, 131 Pseudo-length, 136 Pseudometric. 32 Quadratic t,irrie. 62 Radius, 202 R.411, 39 Rancloni Accpss SIaclii~ic, 59 Real-R-All. 60 Rectilinear Steiricir Problcrii. 89 Regular, 12 Relativc neighbor, 104 Relative ueighl-)orliood graph. 103 Relative Keighborliood Problem.

104 RNG, 103 Root, 178 Root of t,he tree. 178 Rooted binary tree, 187 Rooted K-tree. 178 Rooted t,ree, 186 Rooting a tree. 187 Sausage, 91 Score matrix, 142 Scoring system, 142 Searching. 6.5 Selection. G-l Sequence. 133 Sequence space. 133 Shortost path. 46

Sliortpst Pa th Problem. 46 Shortest supersequericc, 146 Single linkage c l~s t~e r ing . 220 Size of a full colriponent, 102 SLIT. 24, 33 Solution, 38 Sorting. 64 Spanner, 121 Spanning tree. 16, 199 Spaririirig tree problem, 20 Split, 182 Split riiet,ric. 184 Star , 15 Star alignment. 133 Steiner's Yrtn-ork Prohlcm. 114 Steirier's Prohle~n. 22 Steiner's Problem in Networks, 49 Steirier's Problem

discrete version, 71 restricted. 93 n.eiglited inodificatiori, 97

Steiner 111111. 38 Steiner lliriilnal Tree! 24. 33 Steiner point, 24, 33 Steirier ratio. 76 Stciiier ratio of sequence spaces,

138 Steilier ratio of tlic Phylogerietic

space. 137 Stern~na, 170 Stirliiig's approximat,ion, 63 Stirling's formula. 63 Stirling's irieyualities. 63 String. 133 Subgraph. 13

induced. 13 Suhspacr. 32 Suhtree, 13 Successor, 183

immediate. 18.1, Sum-of-pairs alignment, 153 S11pertr.w. 229

Super trce Ploblern. 229 SJ inimetilc dlffercnce, 183 T a d , 192 Taxon 159 Taxonom! 160 The Consmsus Trce Problem 227 Tirne c o m p l ~ x i t ~ , 61 TLI 60 Tolricclll point, 2 207 Totnl leilgth, 33 Trax elirig Salesmm P i o b l ~ r n , 110 Tiaveling Salesman Tour 110 Tree 14 Trce alignrncnt, 133 Tree foi S. 178 Tree

labelled, 177 Tr imgle inequalit\, 32

wealel folm 106 Trianguliitioii 106 TST 110 Tuiirig \fachine. 60 Ultrarnetiic 196 Ultr a ~ n e t i ic b p x e , 72 Union of grnphs, 13 CPGLIX, 221 I'ertex, 12 I7LSI la! out. 89 Ihronoi cell 19. 70 \-or onoi diagrain. 19. 70 IVeiszfeld algoiithrri. 7. 86 Mhid, 133 TTToid garnc. 197 IT or st-caw pel for mnnce, 63 M'PGIIA. 221