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Hammer P.L., Rudeanu S. — Boolean methods in operations research and related areas
Hammer P.L., Rudeanu S. — Boolean methods in operations research and related areas

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Название: Boolean methods in operations research and related areas

Авторы: Hammer P.L., Rudeanu S.

Аннотация:

In classical analysis, there is a vast difference between the class of problems that may be handled by means of the methods of calculus and the class of problems requiring combinatorial techniques. With the advent of the digital computer, the distinction begins to blur, and with the increasing emphasis on problems involving optimization over structures, the distinction vanishes.
What is necessary for the analytic and computational treatment of significant questions arising in modern control theory, mathematical economics, scheduling theory, operations research, bioengineering, and so forth is a new and more flexible mathematical theory which subsumes both the classical continuous and discrete ilgorithms. The work by Hammer (Ivanescu) and Rudeanu on Boolean methods represents an important step in this direction, and it is thus a great pleasure to welcome it into print. It will certainly stimulate a great deal of additional research in both theory and application.


Язык: en

Рубрика: Наука/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 329

Добавлена в каталог: 08.06.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mu$-closure      174
Absolutely maximal internally stable set      209 218
Absolutely maximal matching      238
Absolutely minimal externally stable set      210 224
Absolutely minimal separating set      242
Acceptable state      295
Adjacency matrix      175
Adjoint of a Boolean matrix      14
Aiidreoli, G.      47
Akers Jr., S.B.      47
Algebraic transitive closure      174
All-integer mathematical programming      159
Analysis of multi-terminals      199
Anghel, D.      280
Angstl, H.      240
Anti-chain      263
Appleby, J.S.      276
ARC      172
Arc-capacity      258
Arithmetic form of a Boolean expression      6
Arnold, B.H.      6
Assignment of numbers to vertices      277
Assignment problems      237 246ff.
Balakran      40
Balas, Ј.      49 268 275 276
Balinski, M.L.      48 159
Bantzig,G.B.      II 92 170 193 235 248 263 266 278
Barr, M.      47
Basic algorithm for pseudo-Boolean programming      113ff.
Basic solution of a pseudo-Boolean inequality      56
Bazilevskil, Ju.Ja.      47
Beale, E.M.L.      48 159
Beaufays, O.      40
Beljinan, R.      II IV 48 113 278
Ben — Israel, A.      48 159
Benders, G.F.      48
Berge, C.      2 146 172 209 226 246
Berghiua, J.      270
Bernstein, B.A.      47
Bertier, P.      49
Bipartite graph      237 ff.
Birkhoff, G.      47
Blake, D.V.      276
Boole, G.      47
Boolean algebra      6 16
Boolean conjunction (multiplication)      4 16
Boolean determinant      14
Boolean disjunction      2 3
Boolean equation      2 23ff.
Boolean expression      7 8
Boolean function      6ff. 24
Boolean function generated by an expression      8 24
Boolean matrix      10ff.
Boolean multiplication (conjunction)      3 4 16
Boolean negation      3 16
Boolean ring      20
Bossert, W.H.      276
Breuer, M.A.      288
Burlacu, E.      280
Byser, H.J.      257
Camion, P.      48 40 75ff. 97ff. 109ff. 194 196 197
Canonical form of a linear pseudo-Boolean equation      49
Canonical form of a linear pseudo-Boolean inequality      55
Cardot, C.      286
Caroline, K.      48
Carruccio, E.      40
Cartwright, D.      172—174
Carvallo, M.      6 22 39 40
Catchpole, A.R.      48
Center of a graph      175
Cetkovic, S.      47
Chain in a partially ordered set      263
Characteristic equation      82ff.
Characteristic exponent of a Boolean matrix      13
Characteristic function      83 ff.
Characteristic vector of a subset      212 228
Charnes, A.      48 151 159
Chromatic decomposition      210 228
Chromatic number      211
Circuit      173
Circulation theorem      262
Closure operator      182
Compatible sets      295
Complete elementary conjunction      9
Complete elementary disjunction      10
Complete graph      174
Conjunctive canonical form of a Boolean function      10
Conjunctive form of a Boolean function      8
Connected graph      174
Constantinescu, P.      100
Converse dominating set      210
Converse domination number      210
Cooper, W.W.      151
Couturat, L.      47
Covering matrix      229
Covering of conjunctions      289
Critical set      244
Csima, J.      276
Culik, K.      40
Cut in a network      1 259
d-externally stable set      224
d-internally stable set      218
De Morgan, A.      38 266
Decomposition matrix of a graph      185
Deficiency of a bipartite graph      244
Del Re, A.      47
Deleanu, A.      277
Denis — Papin, M.      6 83 286
Desbazeille, G.      279
Diameter of a graph      175
Dilworth, A.P.      263 265
Dinkelbach, W.      151
Diophantine equation      194
Discrete variable problems      170
Disjointed form of the characteristic function      95
Disjunctive canonical form of a Boolean function      9
Disjunctive form of a Boolean function      8
Distances in graphs      175
Dixit, A.K.      IV
Doig, A.G.      48
Dragan, P.      IV
Dragu§in,C.      199
Dreyfus, S.E.      48 278
Dual of an undirected graph      238
Dubisch, R.      6
Dulmage, A.L.      257
Egervary, J., I      248
Elementary circuit      173
Elementary conjunction      8
Elementary disjunction      8
Elementary path      173
Elngorin, M.Ja.      40 47
Elongation of a vertex      175
Elspas, B.      40
Extension of the basic algorithm for minimization      129ff.
Externally stable set      209 220ff.
Fabia.i, Cs.      IV 109
Family of solutions      45 ff. 55
Faure, R.      6 49 83 286
Fixed variable of a family of solutions      55
Flanient, C.      286
Flegg, H.G.      6
Flood, M.M.      193
Flow in a network      1 258
Ford Jr., L.R.      1 257 258 260
Fortet, R.      II 48 75ff. 97ff. 103 113 114 127 194 235 268 270
Four-colour|ng problem      234ff.
Fractional pseudo-Boolean programming      151 ff.
Fragmentary Hamiltonian circuit      195
Free Boolean algebra      198
Free incidence matrix      199
Free unitary incidence matrix      199
Fridshall, R.      289
Fulkerson, D.R.      1 193 257 258 260 232—264 266 267
Gale, D.      261
Gaspar, T.      IV 280
General solution of a Boolean equation      34
Generalized pseudo-Boolean programming      301 ff.
Ghouila — Houri, A.      172
Gill, A.      294
Global minimum of a pseudo-Boolean function      102
Globally minimizing point of a pseudo-Boolean function      102
Gomory, R.E.      160 235
Goodman, A.W.      47
Goodstein, R.L.      47
Gotham, A.      289
Gotlieb, C.C.      276
Goto, M.      40 47 298
Graph      172
GrebenScikov, V.N.      32
Greniewski, H.      286
Grigorian, Ju.I.      40
Hakimi, S.L.      224
Hall Jr., M.      257
Hall, P.      246 254 257
Halmos, P.R.      257
Hamiltonian circuit      173
Hamiltonian path      173
Hammer (Ivanescu), P.L.      1 48 82 83 102ff. 113 227 229 233 235 249 258 265 277 288
Harary,F.      172—174
Harmon, H.B.      276
Harper, L.H.      277 278
Healy Jr., W.C.      48
Hoffman, A.J.      257 262 263 265 266
Hungarian method for the transportation problem      248
Idempotent matrix      14
Ihde, G.-B.      II
Implicant of a Boolean function      288
Inagaki,Y.      II 287 298 299
Incidence matrix      175
Independence number      209
Independent set      209
Integer mathematical programming      159
Internally stable set      209 212ff.
Interpolation formula      10 22
Irredundant solution of a Boolean equation      35ff.
Irredundant solution of the characteristic equation      93ff.
Itoh, M.      40 47
Ivanescu, P.L.      see “Hammer (Ivanescu) P.L.”
Jevons, S.      47
Johnson, S.M.      193
Johnson, W.W.      47
Juncosa, M.L.      289
k-distinguishable sets      295
Karp, R.M.      193
Kaufmann, A.      6 172 189 192 286
Kernel      210 225
Kirchgassner, K.      276
Klir, J.      40
Knapsack problem      278
Koegst, M.      IV
Komamiya, Y.      47
Konig, D.      172 246 267
Krai, J.      II 299 300
Kuhn, H.W.      248 257
Kuiken, C.      48
Kunzi,H.P.      IV 159
Kuratowski, K.      182
Lagrangean multipliers      122ff. 141
Lalan, V.      40 47
Land, A.H.      48
Latin matrix      189
Latin multiplication      188
Latin product      188 189
Ledley, R.S.      40
Length of a path      173
Leontieff, W.W.      286
LGwenheim, L.      23 38 39 47
Lindsey, J.H.      278
Linear (continuous) programming      164ff.
Linear pseudo-Boolean equation      49ff.
Linear pseudo-Boolean inequality      54ff.
Linear pseudo-Boolean programming, accelerated      106
Little, J.D.C.      48
Local minimum of a pseudo-Boolean function      135
Locally minimizing point of a pseudo-Boolean function      135
Location of plants      282
Loop      173
Lower bounds on arc flows      260
Lunc, A.G.      13 14 199 287
Lupulescu, M.      280
MaciSSak,K.      151
Maghout,K.      159 164 169 176 204 212 214 220 221
Maitra, K.K.      40
Malgrange, Y.      49 83 189 217
Malstrova, T.L.      288
Mann, H.B.      257
Manne, A.S.      282 283
Marcus, S.      215
Martelotta, R.      47
Martos, B.      151
Matching of a graph      237
Maximal anti-chain      265
Maximal clique of a graph      147
Maximal flow      258 259
Maximal internally stable set      146 209
Maximal matching      238
McCluskey Jr., E.C.      212 277 288 290 293 295
Mealy, G.      294
Median, S.      294
Mendelsohn, N.S.      257
Method of bifurcations      39 ff.
Mihoc, Gh.      268 275
Minimal chromatic decomposition      211
Minimal cut      259
Minimal decomposition into chains      263
Minimal externally stable set      146 210
Minimal separating set      242
Minimax of a pseudo-Boolean function      148 ff.
Minimization of a Boolean function      287ff.
Minimization of a pseudo-Boolean function      102ff.
Minimization of the number of states      294ff.
Minimum of a pseudo-Boolean function      102
Mititelu, St.      199
Mixed integer-continuous mathematical programming      162ff.
Moisil, Gr.C.      IV 7 199 293 294 301
Morgenstern, O.      2
Murty, K.G.      48
Murty, U.S.R.      II 258
Nadler, M.      40
Near-minima of a pseudo-Boolean function      147
Nemeti,L.      92
Network      258
Newman, E.A.      276
Nghiem, Ph.T.      49
Node      172
Nonlinear pseudo-Boolean equations and inequalities      82 ff.
Nordio, S.      40
Norman, R.Z.      172—174
North, J.H.      289
Number of external stability      210 224
Number of internal stability      209 218
Oettli,W.      159
Operations with Boolean matrices      10
Ordering of ${B}_{2}$      10
Ordering of a Boolean algebra      18
Ore, O.      172 209 245 246 257
Parametric solution of a Boolean equation      33ff. 47
Parker, W.L.      47
Partial order      19
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