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Foulds L.R. — Combinatorial optimization for undergraduates |
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Предметный указатель |
Activity networks, activity-arc model 155
Activity networks, activity-node model 148—155
Activity networks, earliest finish time 150
Activity networks, earliest start time 150
Activity networks, latest finish time 150
Activity networks, latest start time 150
Acyclic see "Graph"
Adjacency graph see "Graph"
Adjacent 210
Aeneid 3
Aho, A.V. 218
Algorithm 113
Appel, K.I. 215 222
ARC 210
Archimedes 3
Assignment problem 68—76
Assignment problem, Hungarian method 72
Backtracking 107
Balas' method 89 218
Basis 20
Bazaara, M.S. 217
Bell, E.J. 217
Bellman, R.E. 103 218
Bipartite see "Graph"
Bondy, J.A. 222
Bound, greatest lower 4
Bound, least upper 4
Bound, lower 4
Bound, upper 4
Branch 210
Branch and bound 84
Breakthrough 137
Busacker, R.G. 220
Calculus of variations 3
Canonical form 20 23
Car pooling 185—192
Car pooling, nearest-point procedure 186
Car pooling, tree collapsing heuristic 190
Car pooling, triangular heuristic 188
Chromatic number 215
Clarke — Wright heuristic see "Vehicle scheduling"
Closest-insertion heuristic see "Traveling-salesman problem"
Cofactor 205
Combinatorial mathematics 111
Combinatorial optimization 3 111
Combinatorial optimization, fundamental algorithm of 11
Complementary slackness 40
complexity 111—113
Component 121
Component analysis strategy see "Heuristics"
Connected see "Graph"
Construction strategy see "Heuristics"
Convex hull 174
Cook, S.A. 218
Cover 214
Criterion for optimality 30
Critical path method 150
Cutting planes 93
Daellenbach, H.G. 217
Dakin's method 84 217
Dantzig, G.B. 217
Decision tree 87
Degeneracy 31
Degree see "Vertex"
Deltahedron method see "Facilities layout"
Deo, N. 222
Descartes 114
Determinants 205
Determinants, properties of 207
Diagraph 211
Diagraph, connected 212
Diagraph, strongly connected 212
Dijkstras' method 125 219
Dominating set 214
Dreyfus, S.E. 218
Dual 35
Dual simplex method 42 100
Duality 34—48
Dynamic programming 103—110
Earliest finish time see "Activity networks"
Earliest start time see "Activity networks"
EDGE 210
Edmonds, J. 218
Embedded 214
Euclid 114
Euler 213 214
Evolutionary trees 193—201
Evolutionary trees, coalescement 197
Evolutionary trees, maximum parsimony 194
Evolutionary trees, nucleotide sequences 194
Evolutionary trees, Steiner points 198
Excess capacity 135
Extreme point 20
Extremum, global 4
Extremum, local 9
Facilities layout 10 161—168
Facilities layout, deltahedron method 165
feasible 19
Float, free 155
Float, total 154
Flow, backwards 136
Flow, conservation of 132
Flow, forward 136
Floyd's method 127 219
Ford, L.R. 220
Foulds, L.R. 216 219 221 222
Four Colour Conjecture 214
Fulkerson, D.R. 220
Garey, M.R. 219
Garfinkel, R.S. 217
Gass, S.I. 217
Gauss — Jordan elimination 24 209
Geometric heuristic see "Traveling-salesman problem"
Gomory's method 97 218
Gomory's method, Gomory cut 100
Gowan, P.J. 220
Graham, R.L. 222
Graph 210
Graph theory 210
Graph, acyclic 212
Graph, adjacency 163
Graph, bipartite 214
Graph, connected 212
Graph, Hamiltonian 214
Graph, k-connected 212
Graph, maximally planar 214
Graph, partial 211
Graph, planar 214
Graph, spanning 211
Graph, weighted 215
Greenberg, N. 217
Hadley, G. 218
Haken, W. 215 222
Hamilton 214
Hamiltonian 214
Hamiltonian cycle 170
Hamiltonian shortest path 5
Harary, F. 222
Hendy, M.D. 222
Heuristics 113—117
Heuristics, component analysis strategy 115
Heuristics, construction strategy 114
Heuristics, design of 116
Heuristics, improvement strategy 115
Heuristics, learning strategy 115
Hopcroft, I.E. 218
Hu, T.C. 220
Hungarian method see "Assignment problem"
Implicit enumeration 84
Improvement strategy see "Heuristics"
| incident 210
Independent set 214
Integer programming 80—102
Integer programming, all integer problem 82
Integer programming, general problem 81
Integer programming, mixed-integer problem 82 98
Integer programming, zero-one problem 82
Jarvis, J.J. 217
Johnson, D.S. 219
Junction 210
k-connected see "Graph"
Karp, R.M. 219
Klein, M. 220
Koenig's Theorem 74
Koenigsberg bridge problem 213
Kruskals' method see "Minimal spanning trees"
Labeling method see "Maximum-flow problem"
Latest finish time see "Activity networks"
Latest start time see "Activity networks"
Lawler, E.L. 216 217
Learning strategy see "Heuristics"
Least-cost method see "Transportation problem"
Leibnitz 114
Lewis, P.M. 221
Line 210
Linear programming 12—43
Linear programming, graphical solution 14
Linear programming, standard form 17
Linear programming, two-phase method 26
Link 210
Lockyer, K.G. 221
Matching 214
Matching, perfect 214
Matrix 202
Matrix, adjacency 215
Matrix, adjoint 207
Matrix, cofactor 207
Matrix, identity 202
Matrix, incidence 215
Matrix, inverse 208
Matrix, multiplication of 204
Matrix, nonsingular 208
Matrix, properties of 204
Matrix, square 202
Matrix, subtraction of 204
Matrix, sum 203
Matrix, symmetric 5
Matrix, transpose of 203
Matrix, zero 202
Max-flow, min-cut Theorem 135
Maximally planar see "Graph"
Maximum, global 4
Maximum, local 9
Maximum-flow problem 132
Maximum-flow problem, labeling method 135 140—141
Minieka, E. 220
Minimal cost network problem 10 142
Minimal cut 135
Minimal spanning trees 118 196
Minimal spanning trees, Kruskals' method 120 219
Minimal spanning trees, Prim's method 121 199 219
Minimum, global 4
Minimum, local 5
Minor 205
Mueller-Merbach, H. 219
Multigraph 211
Multiple optima 30
Murty, U.S.R. 222
Nearest-neighbor heuristic see "Traveling-salesman problem"
Nearest-point procedure see "Car pooling"
Nemhauser, G.L. 217 218
Network 211
Node 210
Northwest-corner method see "Transportation problem"
NP-completeness 112
Optimal solution 3
Optimization 3
Optimization, linear 12—43
Optimization, nonlinear 12
Papadimitriou, C. 216
Pappas 114
Partial graph see "Graph"
Partial subgraph 212
Path 212
Penny, E.D. 222
PERT 156
Phylogenies 193
Pivot 24
Planar see "Graph"
Point 210
Policy 107
Polynomial time 112
Precedence, activities 148
Precedence, diagram 148
Prim's method see "Minimal spanning trees"
Primal 35
Pseudograph 211
Queen Dido 3
Recursion, backwards 108
Recursion, forward 106
Recursive equations 107
Reducibility 112
RETURN 104
Robinson, D.F. 216 221
Rosencrantz, D.J. 221
Rounding 82
Scalar, multiplication 203
Scalar, product 203
Shortest path problems 103 123
Simplex method 12 20—34
Sink 211
Smith, D.K. 220
Solution, basic 20
Solution, degenerate 20 31
Solution, feasible 4
Source 211
Spanning graph see "Graph"
Spanning subgraph 212
Stage 104
State 104
Stearns, R.E. 221
Steiglitz, K. 216
Steiner problem in phylogeny 198
Stepping-stone method see "Transportation problem"
Strongly connected see "Digraph"
Subgraph 211
Sweep heuristic see "Vehicle scheduling"
Taha, H.A. 217
Trail 212
Transportation problem 10 48—64
Transportation problem, balanced 50
Transportation problem, least-cost method 56
Transportation problem, northwest-corner method 54
Transportation problem, stepping-stone method 60
Transportation problem, unbalanced 50
Transportation problem, Vogel approximation method 56
Transshipment problem 64—68
Transshipment problem, buffer stock 66
Traveling-salesman problem 10 170—178
Traveling-salesman problem, closest-insertion heuristic 196
Traveling-salesman problem, geometric heuristic 174
Traveling-salesman problem, nearest-neighbor heuristic 171
Tree-collapsing heuristic see "Car pooling"
Triangular heuristic see "Car pooling"
Two-phase method see "Linear programming"
Ullman, I.D. 218
Variables, artificial 24
Variables, basic 20
Variables, nonbasic 20
Variables, slack 17
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