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Ruskey F. — Combinatorial generation
Ruskey F. — Combinatorial generation



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Название: Combinatorial generation

Автор: Ruskey F.

Аннотация:

These lists are not only interesting but can be extremely useful. Nearly every computer scientist and mathematician has encountered some instance where they solved a problem simply by listing all the possibilities and checking for a desired property. One can find applications of the ideas in this book to circuit design, statistical computing, chemistry, and operations research, just to name a few.


Язык: en

Рубрика: Computer science/Алгоритмы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 289

Добавлена в каталог: 22.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A-order      107
Alphabet      11
Alternating permutation      111
Anchor      44
Antichain      19
Antimatroid      20 206 241
Antimatroid, basic words      20
Antipodal chain      191
APPEND      12
Arboricity      247
AVL tree      108
B-order      107
B-tree      86 108
B-tree, generating all      86—89
Backtracking, non-recursive algorithm      43 44
Backtracking, recursive algorithm      43
Backtracking, tree      43
Bag      15
Basic word graph      206
Bell number      17 35 89 90 93 109 159
BEST (Backtracking Ensuring Success at Terminals)      8 9 47
Bicentral tree      83
Binary tree      74 112
Binary tree, complete      102
Binary tree, Gray code      138 142 175
Binary tree, rotation      142
Binary tree, unordered      112
Binary trees, random generation of      252
Binomial coefficient      13
bitstring      11
Bracelet      232
Buckyball      204
Burnside’s Lemma      32 215
Campanology      189 205
CAT (Constant Amortized Time)      8 9
Catalan number      21 36 74 146
Catalan numbers      21
Cayley graph      33 189
Cayley graph over Abelian group      199
Center      83
Centroid      83
Chain      19
Change-ringing      189
Chinese Rings      178
CLIQUE      28 246 247
Closeness relation      116
Cluster      125
Co-lexicographic order      55
Colex (or RL) Superiority Principle      59
Comb      134
Combination      226
Combination of a multiset      71
Combination, Gray code      185
Combination, random      249
Combinations, Gray code      125
Combinatorial Gray code      116
Combinatorial Gray code, cyclic      116
composition      13 106 149
Composition with restricted parts      71
Composition, Gray code for      149—153
Concatenate      12
Concave      35
conjugate      16 109
Conjugate of numerical partition      37
Constant time initialization      34
Context-free language      232 252
Contingency table      71 110
Cover relation      19
Coxeter graph      195
Cubic graph      178 241
Cut      246
Cutset      246
CYCLE      246
Cycle lemma      107 252
de Bruijn, cycle      232
De Bruijn, graph      220
De Bruijn, sequence      220
De Bruijn, torus      232
Degree of a vertex      26
Degree sequence      110
Depth-first numbering      29
Depth-first search      29 209
Depth-first-search      243
Derangement      14 35 106 181 252
Digraph, connected      27
Digraph, strongly connected      27
Digraph, tournament      28
Direct algorithm      121
Distributive lattice      203
Dominating property      74
Dominoe      229
Dominoes      207
Euler pentagonal number theorem      37
Eulerian number      15
Eulerian, cycle      208 210
Eulerian, graph      208
Extension      19
Extension-rotation algorithm      176—178
extent      189 204
Ferrer’s diagram      16
Fibonacci number      33
Free tree      78 82 83 112
Free tree, generating all      82—86
Free tree, random generation of      252
Function      12
Function, bijection      12
Function, injective      12
Function, surjective      12
Graph      26
Graph, 1-Hamiltonian      205
Graph, acyclic      26
Graph, acyclic orientation      27 186 205
Graph, adjacency lists      29
Graph, adjacency matrix      28
Graph, arboricity of      247
Graph, automorphism group of      31
Graph, automorphism of      26
Graph, bipartite      27 240 241
Graph, Cayley      53
Graph, clique      28
Graph, coloring      28 52
Graph, complete ($K_{n}$)      27
Graph, complete bipartite ($K_{m,n}$)      27
Graph, connected      26
Graph, connected component      29
Graph, cube of      27 204 206
Graph, cubic      26 178 240
Graph, directed Cayley      33
Graph, generating non-isomorphic      236—238
Graph, grid      204
Graph, Hamilton-connected      28
Graph, Hamilton-laceable      28
Graph, Hamiltonian      28 37
Graph, hypercube ($Q_{n}$)      27
Graph, hypo-Hamiltonian      28
Graph, independent set      28
Graph, pancyclic      28
Graph, planar      247
Graph, prism of      27 205
Graph, product of      27
Graph, random      252
Graph, regular      26
Graph, shuffle-exchange      206
Graph, spanning subgraph of      28
Graph, square of      27 204—206
Graph, subgraph of      26
Graph, undirected Cayley      33
Graph, unicyclic      24 241
Graph, vertex cover      28
Graph, vertex-transitive      26 31
Graphical partitions      110
Gray code for binary trees      175
Gray code for combinations      125 185
Gray code for multiset permutations      146
Gray code, binary reflected (BRGC)      116 178 229
Gray code, binary tree      138 142
Gray code, composition      149
Gray code, monotone      190
Gray code, numerical partition      153
Gray code, set partition      159
Gray code, uniform      122
Gray code, well-formed parenthesis      139
Greedoid      241
Group      26 30
Group, abelian      31 199
Group, action      31
Group, cyclic      30 232
Group, dihedral      30 232
Group, generating set for      33
Group, hypo-octohedral      31
Group, order of      30
Group, order of an element in      30
Group, subgroup      30
Group, symmetric      30 31
Group, transitive      31
Hamilton cycle      28 53
Hamilton laceable      179
Hamilton path      28 204
Hamiltonian cycle, algorithm for      176—178
Hamming distance      11 178
Hasse diagram      19
Height-balanced (AVL) tree      113
Hexomino      51
Hypercube      114 202 203 210
Hypercube ($Q_{n}$)      27 117
Ideal      20
Ideal, generating all      101—103
In-tree      23 208
Independent set      28
Independent set, maximal      246
Index of a permutation      14
Indirect algorithm      121
inversion      14 106
Inversion string      111
Inversion, string      68 106 111
Inversion, table      111
Inversion, vector      111
Involution      15 106 111 230
Knight’s tour      52
Labelled trees      78
Latin rectangle      106 106
Lattice      19 241
Lattice, distributive      20 203
Lexicographic order      55
Linear algorithm      9
Linear extension      19 27 52 110 113
Linear extension, generating all      99—101
Linear extension, Gray code for      165—174
Linear feedback shift register (LFSR)      228—229
LIST      11
List, append      12
List, concatenation of      12
List, interface between      12
List, prepend      12
Log-concave      35
Logarithmically concave      73
Loopless      5
Loopless algorithm      121
Lyndon, factorization      222
Lyndon, word      185 214 216 217 220 227 230 231 233
Lyndon, word, random      250
Magic square      110
Matching, perfect      247
Matrix tree theorem      194
Matroid      247
Matroid, listing bases of      247
Maximal independent set      247
Memoryless      5 56 67
Middle two levels problem      182
Moebius, function      215
Moebius, inversion      17 215
Monotone runs      106
Multinomial coefficient      15
Multiplicity representation      94 109 238
Multiset      15
Multiset permutations      185
Multiset, combinations of      71
Multiset, specification of      68
Murasaki diagram      iii
N-queens problem      41
Natural representation      94 109
Necklace      213 216 217
Necklace of a string      222
Necklace, factorization      222
Necklace, random      250
NUMBER      11
Numerical partition      93 113
Numerical partition into distinct parts      109
Numerical partition into odd parts      109
Numerical partition, conjugate of      37
Numerical partition, Gray code      153
Numerical partition, random      251
Ordered forest      107
Ordered tree      112
Ordered tree, degree of a node      20
Orthogonality relation      107
Out-tree      23 208
Parity difference      14 181
Partially ordered set      19
Partite set      27
Partition      16
Partition, binary      109
Partition, numerical      16 238
Partition, numerical, conjugate of      16
Partition, part of      93
Partition, set      17 225
Partition, set, block of      17
Partition, set, with given block sizes      164
Partitions, graphical      110
Pascal’s triangle      13
Pendant vertex      26 154
Pentomino      44
Permutation      14 111
Permutation of a multiset, random      250
Permutation, alternating, Gray code for      164
Permutation, cycle      106
Permutation, cycle notation      14
Permutation, cycle representation      34
Permutation, cycles in      14
Permutation, derangement      14 35 106 181 252
Permutation, even      14
Permutation, index of      14
Permutation, inverse      34 35
Permutation, inverse of      14
Permutation, inversion      14 35 106
Permutation, inversion string of      68 111
Permutation, involution      15 35 106
Permutation, k-permutation      15
Permutation, odd      14
Permutation, one-line notation      14
Permutation, parity of      14
Permutation, random      249
Permutation, rosemary      111
Permutation, run      15
Permutation, sign      34
Permutation, sign of      14
Permutation, transposition      14
Permutation, up-down      15 106
Permutohedron      19
PET      61
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