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Steele J.M. — Probability Theory and Combinatorial Optimization
Steele J.M. — Probability Theory and Combinatorial Optimization



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Название: Probability Theory and Combinatorial Optimization

Автор: Steele J.M.

Аннотация:

This monograph provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization. The questions that receive the most attention are those that deal with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings. Still, there are several nongeometric optimization problems that receive full treatment, and these include the problems of the longest common subsequence and the longest increasing subsequence. The philosophy that guides the exposition is that analysis of concrete problems is the most effective way to explain even the most general methods or abstract principles.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 159

Добавлена в каталог: 18.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adler, R.      49
Aho, A.V.      18
Ajtai, M.      141
Aldous, D.      25 94 96 100 117
Alexander, K.S.      13 24 67 100 108 109
Alon, N.      24 112
Alpern, S.      50
Alternating chain lemma      136
Apostolico, A.      18
Assignment problem      77 135
Assignment problem, greedy algorithm      77
Assignment problem, linear programming, connection      81
Assignment problem, matching theory method      78
Assignment problem, Talagrand's tail bound      139
Avis, D.      93
Avram, F.      49 108 110 114 118
Azuma's inequality      5
Azuma, K.      4
Bailey, T.      49
Baldi, P.      112
Bartholdi, J.J.      43
Beardwood — Halton — Hammersley (BHH) theorem, general case      34
Beardwood — Halton — Hammersley (BHH) theorem, uniform case      33
Beardwood, J.      33
Bellman, R.      40
Bern, M.      117
Bersekas, D.R.      94
Bertsimas, D.      108 110 114 118
Bickel, P.      110
Bingham, N.H.      25
Bland, R.      95
Bollobas, B.      24 132
Breiman, L.      110
Burkholder's inequality      45
Burkholder, D.L.      45
Central limit theory (CLT), conditioning methods      110
Central limit theory (CLT), minimal spanning tree      108
Chvatal      1 4 94
Coffman, E.G., Jr.      141
Concentration inequality for the TSP      29
Concentration inequality smooth functionals      62
Concentration inequality space-filling curve heuristic      44
Convex distance      120
Dancik, V.      3
DeBruijn, N.G.      21
Deken, J.P.      3
Delaunay triangulation      95
Devroye, L.      93
Doob, J.      5
Dyer — Frieze — McDiarmid inequality      84
Dyer, M.E.      82
Dynamic programming      16
Eddy, W.F.      99
Efron, B.      124
Eggert, M.      3
Epstein, D.      117
Erdoes — Szekeres theorem      6 17
Erdoes, P.      6 21 24 112
Euclidean functionals      53
Expander graphs      137
Fekete, M.      2
Few, L.      50
Flipping lemma      10
Flipping method      10 127
Fredman, M.L.      17
Frenk, J.B.G.      93
Frieze, A.M.      11 13 82
Gao, J.      43
Garsia, A.      49
Gaussian tail bound for the TSP      124
Geometric subadditivity      54 60
Goddyn, L.      50
Goemans, M.X.      94
Groneboom, P.      116
Guerra, C.      18
Halton, J.H.      33 41
Hammersley, J.M.      6 26 33
Hausdorff distance      132
Hereditary sets      131
Heurter, I.      116
Hilbert, D.      44
Hille, E.      25
Hirshberg, D.S.      18
Hochbaum, D.      25
Hoeffing, V.      4
Hsing, T.      116
Hunt, J.W.      18
Imai, H.      49
Increasing-subsequence problem      6 75 125
Increasing-subsequence problem, concentration inequalities      10 125
Increasing-subsequence problem, sequential selection      24
Isoperimetric inequality      119
Isoperimetric inequality, Hamming distance      61
Jaillet, P.      65 72
Kahane, J.-P.      49
Kakutani, S.      49
Karloff, H.J.      50
Karp's partioning algorithm      40
Karp, R.M.      35 40 41 50 91 93 137
Kerov, C.V.      10
Kesten, H.      76 109 117
Kingman, J.F.C.      18
Kodialam, M.S.      94
Komlos, J.      141
Kruskal, J.B.      24
Kurtzburg, J.M.      78
Lai, C.W.      93
Lazarus, A.      94
Leader, I.      132
Lee, S.      109 117
Leighton, T.      141
Lens geometry for the MST      107
Leuker, G.S.      141
Lindvall, T.      36
Logan, B.      10
Long-common-subsequence problem      1
Long-common-subsequence problem, algorithms      18
Long-common-subsequence problem, tail bound      6
Lovasz, L.      112
Markov-chain Monte Carlo      140
Maurey, B.      24
McDiarmid, C.J.H.      24 82 93
McKay, D.B.      3
Meyers, E.W.      18
Mezard, M.      76 94
Milman, V.D.      24
Milne, S.C.      49
Minimal spanning tree (MST)      97
Minimal spanning tree (MST), central limit theory      109
Minimal spanning tree (MST), degree theorem      99
Minimal spanning tree (MST), power-weighted edges      99
Minimal-matching problem      63
Minimal-matching problem, two samples      141
Objective method      96
Papadimitriou, C.      40 76
Parisi, G.      76 94
Paterson, M.      3
Peano, G.      44
Phillips, R.S.      25
Platzman, L.K.      43
Poissonization device      25
Polya, G.      25
Ramey, D.B.      108 109
Random graphs      140
Rates of convergence, long-common-subsequence problem      13
Rates of convergence, MST      72
Rates of convergence, rooted-dual method      70
Rates of convergence, TSP means      67
Redmond, C.      68
Renyi, A.      116
Rhee, W.T.      14 24 33 38 59 65 72 75 124
Richardson, D.      76
Rinnooy Kan, A.H.G.      93
Rinnot, Y.      112
Rinsma — Melchert, I.      3
Rooted dual      68
Rooted dual for the minimal matching      70
Rooted dual for the MST      70
Rooted dual for the TSP      68
Sankoff, D.      1 4 24
Schechtman, G.      24
Self-similarity      44
Shamir, E.      24
Shepp, L.A.      10 99
Shor, P.      141
Simple subadditivity      60
Simplex method      82
Snyder, T.L.      50 117
Space-filling curve heuristic      41 125
Spencer, J.      24
Spencer, J.H.      112
Square function      45
Stadje, W.      49
Steele, J.M.      25 41 43 50 75 96 99 100 117 137
Stein, C.      113 124
Subadditive ergodic theorem      19
Subadditive Euclidean functionals      53
Subadditive Euclidean functionals, basic theorem      54
Subadditive sequences      2 21 25
Subadditive sequences, refinements      21
Subadditivity, geometric      60
Subadditivity, geometric from simple      64
Subadditivity, simple      60
Sulanke, R.      116
Syzmansky, T.G.      18
Szegoe, G.      25
Szekeres, G.      6
Talagrand's convex distance      120
Talagrand's isoperimetric inequality, proof      128
Talagrand's isoperimetric theorem      120
Talagrand's isoperimetric theory      119
Talagrand, M.      24 65 119 124
Terada, R.      41
Traveling-salesman problem (TSP)      27
Traveling-salesman problem (TSP), Gaussian tail bound      124
Tusnady, G.      141
van Houweninge, M.V.      93
Versik, A.M.      10
Vohra, R.      93
Voronoi diagram      95
Walkup, D.W.      79 93
Waterman, M.S.      3 4 24
Yao, A.      49
Yukich, J.E.      68 117
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