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Bellman R. — Algorithms, graphs, and computers, Volume 62 (Mathematics in Science and Engineering) |
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Предметный указатель |
Abramson, P. 96
Acceleration of convergence 66 115
Accessibility lists 108 111
Accessibility lists, generation of 160
Adjacency matrix 83 154
Adjacency matrix, powers of 155
Aitken's delta-squared process 66
Algorithm 22 54—61 see
Algorithm, deterministic 57
Algorithm, theory of algorithms 54
Algorithm, tree-building 121
Allocation of resources 114
ARC 37
Array of times 16
Array of times, enlarged 20
artificial intelligence 228 237
Assignment problem 221—226
Ball, W.W.Rouse 138 170 211 231 237
Bandy-ball, game of 138
Bartlett, R.E. 96
Bellman, R. 24 47 96 99 122 171 194 210 212 229 230 231 234 235 236
Bellmore, M. 236
Bentley, D.L. 98 140 141
Berge, C. 37 47
Best current estimates see "Acceleration of convergence"
Billiard ball solution 187
Billiard ball solution use in generating Sawyer graph 188
Bock, F. 96
Boesch, F.T. 48
Branch 7
Branch and bound method 225 236
Branching process 226
Brown, J.R. 234
Calculus 22 52 63
Cameron, S. 96
Cannibals and missionaries puzzle 196—212
Carroll, Lewis 170
Cascade algorithm 99
Cavalli-Sforza, L.L. 38
Chess 232 233 234
Chinese fifteen puzzle 168
Chromatic number 38
Circuit 5
Clark, C.E. 48
Collins, N.L. 237
Combinatorial problems 34
Commuting problem 2 see
Commuting problem solution by enumeration 4—6
Complementary matrix 84
Computer program for pouring puzzle 148 160 164
Computer program for routing problem 82 84 109
Computer program for square root 67
Computer program for travelling salesman problem 219—221
Computers analog 95 192
Computers digital 192
Computers heuristic programming 228 237
Computers parallelization 54 221
Computers programming 57
Computers use in constructing state graphs 192
Congruences 186
Connection matrix 83 111 154
Connectivity matrix 83
Convergence 51 126 129 132 see
Cooke, K.L. 120 140 141 212 230
Cost matrix 152—154 160 206
Cost matrix, modified 165
Courant, R. 38
Court, N.A. 173 195
Coxeter, H.S.M. 38
Critical path 43—46
Dale, E. 237
Dantzig, G.B. 120 121
Davidson, D. 141
Defective coin puzzle 172 235
Detrick, P. 212
Deviation 95
Difficult crossing puzzles 196—212
Dijkstra's algorithm 94 137
Dijkstra, E.W. 94
Dimensionality difficulty 101
Distance between states 162—166 204
Dobbie, J.M. 236
Doublets, game of 170
Dreyfus, S. 24 47 94 95 99 120 121 210
Duality property 131
Dudeney, H.E. 139 172 232
Dynamic programming 47
EDGE 10 33
Edge, directed edge 35
Edwards, A.W.F. 38
Electric generating stations, design of 118
Enumeration 4—9 32 146—148 197 216
Ernst, G.S. 237
Euler circuit 36
Euler graph 37
Euler line 36
Euler, Leonhard 36 48
Extendapawn game 234
Extraneous solution 124
Farbey, B.A. 99 121
Faure, R. 47 171 236
Fazar, W. 48
Feasibility 16 32 81 219 223 228
Fictitious links 85
Finite field arithmetic 85
First approximation 72
flow charts 10 57
Flow charts for square root 69
Floyd, R.W. 121
Four color problem see "Map coloring"
Fraley, R. 212
Fulkerson, D.R. 48 236
Function 22
Functional equations see also "Fundamental equations of routing" "Recurrence
Functional equations for assignment problem 223
Functional equations for cannibals and missionaries puzzle 205
Functional equations for critical path 45
Functional equations for pouring puzzle 156 163
Functional equations for travelling salesman problem 219
Fundamental convergence of successive approximations 126 132
Fundamental elimination of variables 30
Fundamental equations of routing 28 49 85
Fundamental existence of solution 125
Fundamental uniqueness of solution 125 129—131
Gardner, M. 170 173
Gaunt, S. 236
Geodesics 48
Gilbert, E.N. 38
Gluss, B. 235
Golomb, S.W. 233
Graham, L.A. 172 231
graphs 33—39
Graphs, complete 34
Graphs, connected 37
Gruon, R. 47
Haggerty, J.B. 211
Hakimi, S.L. 140
Halsey, E. 120
Hamilton circuits 220 237
Hamilton, W.R. 220
Hammersley, J.M. 38 235 236
Hanan, M. 38
Harary, F. 48
Heuristic programming 228 237
Hitchcock — Koopman — Kantorovich transportation problem 209
Hoffman, W. 95
Howard, R. 99
Hu, T.C. 121
Hurwitz, A. 53
Imbedding 21
| Induction, mathematical 51
Initial approximation 69 73 78
Iteration see "Successive approximations"
Johnson, S.M. 235
Joksch, H.C. 140
Kalaba, R. 95 99 121
Kalah, game of 211
Kaufmann, A. 47 171
Klee, V.L. 96
Knight's Tour 233
Konigsberg bridges, problem 36 230
Kraitchik, M. 171 210 232
Kravitz, S. 48
Kron, G. 122
Kumar, S. 121 212
Labelling algorithms 90—94 99 117 158 191
Labelling algorithms, accelerated 117
Land, A.H. 99 121
Lawler, E.L. 236
Lederberg, J. 237
Lehmer, D.H. 236
Ley, W. 194
LIMIT 52 see
Lindley, D.V. 233
Linear programming 120
Link 10 33
Local degree 37
Logic tree 7
Lower solution 128—129 132—137
Lucas, E. 173
Luccio, F. 122
Lyusternik, L.A. 48
Machine scheduling problem 235
magnetic tapes 110 160
Malcolm, D.G. 48
Map coloring 39 228
Marriage problem 233
Matrix 17
Matrix of coefficients 18
Matrix, associated with a graph 83
Matrix, augmented 18
Matrix, column 17
Matrix, dense 111
Matrix, distance 140
Matrix, element of 17
Matrix, entry in 17
Matrix, full 111
Matrix, product 84
Matrix, row 17
Matrix, sparse 111
Michie, D. 237
Mills, G. 121 122
Minimum cost functions 155
Minimum function 22
Minimum time function 21
Minty, George J. 95
Modular arithmetic 186
Moiseev, N.N. 141
Monotonicity 126
Montalbano, M. 48
Moore, E.F. 99
Munck, A. 48 98
Murchland, J.D. 99 121
Nabeshima, I. 235
Nemhauser, G.L. 236
Newell, A. 237
Newton — Raphson method 63—67
Nicholson, T.A.J. 122
Nim, game of 211
Nim, Moore's 211
Node 33
Nugent, C.E. 236
O'Beirne, T.H. 173 193 195
Obruca, A.K. 236
Optimal planning 114
Optimal trajectory 113
Ore, O. 47 237
Pan, V. Ya. 233
Pape, U. 121
Paper strip algorithm 74 157 165 206
Path 6
Path maximum capacity 96
Path with a given number of junctions 86
Path, most reliable 96
Path, optimal 43 see "Critical
Pavley, R. 95
Pearl, R.M. 96
Pedoe, D. 195
Perelman, Y.J. 195
Perko, A. 121
PERT 45
Phase space 113
Policy 28
Policy, improvement 99
Policy, initial 73 77
Policy, optimal 77 131
Pollack, M. 47 96 99
Pollak, H.O. 38
Polynomials, computing values of 234
Polyominoes 233
Powers of two, calculation of 226
Quickest route problem see "Shortest route problem"
Randolph, P.H. 96
Rapoport, H. 96
Recurrence relations 61 217 227 see
Representations of integers 193
Robbins, H. 38
Roseboom, J.H. 48
Roth, J.P. 122
route see "Path" "Shortest
Ruhlen, L.E. 122
Ruml, J. 236
Saksena, J.P. 121
Sawyer graph 174—195
Sawyer graph, connectedness 180 185
Sawyer graph, number of states 185
Sawyer graph, ring 176
Sawyer graph, spine 176 181
Sawyer, W.W. 195
Scheduling problems 46 213
Scheduling Theory 213
Schwartz, B. 211
Search theory 24 236
Seidel methods 117
Shapiro, J.F. 48 141
Shimbel, A. 99
Shire, P.R. 122
Shorack, G.R. 96
Shortest route problem 4 28 35 see
Shortest route problem, decomposition algorithm 121
Shortest route problem, fundamental equations 85
Shortest route problem, matrix methods 121
Shortest route problem, stochastic 48
Shortest route problem, string model 95
Shortest route problem, tree-building algorithms 121
Smith, C.A.B. 211
Smith, J.M. 171
Sorting 55 59—60
Stairs, S.W. 99 121
State 39—43
State diagram 151 178 198
State graph 42 see
State space 113
State, allowable 198
State, completely accessible 167 185
State, completely reachable 167
State, inaccessible 167 178
State, possibly accessible 167 178
State, reachable 199
Steiner's problem 38
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