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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

Издание: illustrated edition

Год издания: 1987

Количество страниц: 170

Добавлена в каталог: 23.10.2010

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
Alpern, S.      50
Alternating chain lemma      136
Alternating chain lemma      136
Apostolico, A.      18
Apostolico, A.      18
Assignment problem      77 135
Assignment problem      77 135
Assignment problem, greedy algorithm      77
Assignment problem, greedy algorithm      77
Assignment problem, linear programming, connection      81
Assignment problem, linear programming, connection      81
Assignment problem, matching theory method      78
Assignment problem, matching theory method      78
Avis, D.      93
Avis, D.      93
Avram, F.      49 108 110 114 118
Avram, F.      49 108 110 114 118
Azuma, K.      4
Azuma, K.      4
Azuma’s inequality      5
Azuma’s inequality      5
Bailey, T.      49
Bailey, T.      49
Baldi, P.      112
Baldi, P.      112
Bartholdi, J. J.      43
Bartholdi, J. J.      43
Beard wood — Hal ton, Hammersley, (BHH) theorem, general case      34
Beard wood — Hal ton, uniform case      33
Beardwood, J.      33
Bellman, R.      40
Bellman, R.      40
Bern, M.      117
Bern, M.      117
Bersekas, D. P.      94
Bersekas, D. P.      94
Bertsimas, D.      108 110 114 118
Bertsimas, D.      108 110 114 118
Bickel, P.      110
Bickel, P.      110
Bingham, N. H.      25
Bingham, N. H.      25
Bland, R.      95
Bland, R.      95
Bollobas, B.      24 132
Bollobas, B.      24 132
Breiman, L.      110
Breiman, L.      110
Burkholder, D. L.      45
Burkholder, D. L.      45
Burkholder’s inequality      45
Burkholder’s inequality      45
Central limit theory (CLT), conditioning methods      110
Central limit theory (CLT), conditioning methods      110
Central limit theory (CLT), minimal spanning tree      108
Central limit theory (CLT), minimal spanning tree      108
Chvatal      1 4 94
Chvatal      1 4 94
Coffman, E. G., Jr.      141
Concentration inequality for the TSP      29
Concentration inequality for the TSP      29
Concentration inequality, smooth functionals      62
Concentration inequality, smooth functionals      62
Concentration inequality, space-filling curve heuristic      44
Concentration inequality, space-filling curve heuristic      44
Convex distance      120
Convex distance      120
Dancik, V.      3
Dancik, V.      3
DeBruijn, N. G.      21
DeBruijn, N. G.      21
Deken, J. P.      3
Deken, J. P.      3
Delaunay triangulation      95
Delaunay triangulation      95
Devroye, L.      93
Devroye, L.      93
Doob, J.      5
Doob, J.      5
Dyer — Frieze — McDiarmid, inequality      84
Dyer — Frieze — McDiarmid, inequality      84
Dyer, M. E.      82
Dyer, M. E.      82
Dynamic programming      16
Dynamic programming      16
Eddy, W. F.      99
Eddy, W. F.      99
Efron, B.      124 157 158
Efron, B.      124 157 158
Eggert, M.      3
Eggert, M.      3
Epstein, D.      117
Epstein, D.      117
Erdos — Szekeres Theorem      6 17
Erdos — Szekeres Theorem      6 17
Erdos, P.      6 21 24 112
Erdos, P.      6 21 24 112
Euclidean functionals      53
Euclidean functionals      53
Expander graphs      137
Expander graphs      137
Fekete, M.      2
Fekete, M.      2
Flipping lemma      10
Flipping lemma      10
Flipping method      10 127
Flipping method      10 127
Fredman, M. L.      17
Fredman, M. L.      17
FVenk, J. B. G.      93
FVenk, J. B. G.      93
FVieze, A. M.      11 13 82
FVieze, A. M.      11 13 82
Gao, J.      43
Gao, J.      43
Garsia, A.      49
Garsia, A.      49
Gaussian tail bound for the TSP      124
Gaussian tail bound for the TSP      124
Geometric subadditivity      54 60
Geometric subadditivity      54 60
Goddyn, L.      50
Goemans, M. X.      94
Groneboom, P.      116
Groneboom, P.      116
Guerra, C.      18
Halton, J. H.      33 41
Halton, J. H.      33 41
Hammersley, J. M.      6 26 33
Hammersley, J. M.      6 26 33
Hausdorff distance      132
Hausdorff distance      132
Hereditary sets      131
Heurter, I.      116
Hilbert, D.      44
Hilbert, D.      44
Hille, E.      25
Hille, E.      25
Hirshberg, D. S.      18
Hirshberg, D. S.      18
Hochbaum, D.      25
Hochbaum, D.      25
Hoeffing, V.      4
Hoeffing, V.      4
Hsing, T.      116
Hsing, T.      116
Hunt, J. W.      18
Hunt, J. W.      18
Imai, H.      49
Imai, H.      49
Increasing-subsequence problem      6 75 125
Increasing-subsequence problem      6 75 125
Increasing-subsequence problem, concentration inequalities      10 125
Increasing-subsequence problem, concentration inequalities      10 125
Increasing-subsequence problem, sequential selection      24
Increasing-subsequence problem, sequential selection      24
Isoperimetric inequality      119
Isoperimetric inequality      119
Isoperimetric inequality, Hamming distance      61
Isoperimetric inequality, Hamming distance      61
Jaillet, P.      65 72
Jaillet, P.      65 72
Kahane, J. — P.      49
Kahane, J. — P.      49
Kakutani, S.      49
Kakutani, S.      49
Karloff, H. J.      50
Karloff, H. J.      50
Karp, R. M.      35 40 41 50 91 93 137
Karp, R. M.      35 40 41 50 91 93 137
Karp’s partioning algorithm      40
Karp’s partioning algorithm      40
Kerov, C. V.      10
Kerov, C. V.      10
Kesten, H.      76 109 117
Kesten, H.      76 109 117
Kingman, J. F. C.      18
Kodialam, M. S.      94
Komlos, J.      141
Komlos, J.      141
Kruskal, J. B.      24
Kruskal, J. B.      24
Kurtzburg, J. M.      78
Kurtzburg, J. M.      78
Lai, C. W.      93
Lai, C. W.      93
Lazarus, A.      94
Lazarus, A.      94
Leader, I.      132
Lee, S.      109 117
Lee, S.      109 117
Leighton, T.      141
Leighton, T.      141
Lens geometry for the MST      107
Lens geometry for the MST      107
Leuker, G. S.      141
Leuker, G. S.      141
Lindvall, T.      36
Lindvall, T.      36
Logan, B.      10
Logan, B.      10
Long-common-subsequence, algorithms      18
Long-common-subsequence, algorithms      18
Long-common-subsequence, problem      1
Long-common-subsequence, problem      1
Long-common-subsequence, tail bound      6
Long-common-subsequence, tail bound      6
Lovasz, L.      112
Lovasz, L.      112
Markov-chain Monte Carlo      140
Markov-chain Monte Carlo      140
Maurey, B.      24
Maurey, B.      24
McDiarmid, C. J. H.      24 82 93
McDiarmid, C. J. H.      24 82 93
McKay, D. B.      3
McKay, D. B.      3
Meyers, E. W.      18
Meyers, E. W.      18
Mezard, M.      76 94
Mezard, M.      76 94
Milman, V. D.      24
Milman, V. D.      24
Milne, S. C.      49
Milne, S. C.      49
Minimal spanning tree (MST)      97
Minimal spanning tree (MST)      97
Minimal spanning tree (MST), central limit theory      109
Minimal spanning tree (MST), central limit theory      109
Minimal spanning tree (MST), degree theorem      99
Minimal spanning tree (MST), degree theorem      99
Minimal spanning tree (MST), power-weighted edges      99
Minimal spanning tree (MST), power-weighted edges      99
Minimal-matching problem      63
Minimal-matching problem      63
Minimal-matching problem, two samples      141
Minimal-matching problem, two samples      141
Objective method      96
Objective method      96
Objective method, INDEX      159
Objective method, INDEX      159
Papadimitriou, C.      40 76
Papadimitriou, C.      40 76
Parisi, G.      76 94
Parisi, G.      76 94
Paterson, M.      3
Paterson, M.      3
Pcano, G.      44
Pcano, G.      44
Pew, L.      50
Pew, L.      50
Phillips, R. S.      25
Phillips, R. S.      25
Platzman, L. K.      43
Platzman, L. K.      43
Poissonization device      25
Poissonization device      25
Ramey, D. B.      108 109
Ramey, D. B.      108 109
Random graphs      140
Rates of convergence, loiig-commoii-subsequeiice, problem      13
Rates of convergence, loiig-commoii-subsequeiice, problem      13
Rates of convergence, MST      72
Rates of convergence, MST      72
Rates of convergence, rooted-dual method      70
Rates of convergence, rooted-dual method      70
Talagrand, M.      24 65 119 124
Talagrand, M.      24 65 119 124
Talagrand’s convex distance      120
Talagrand’s convex distance      120
Talagrand’s isoperimetric, inequality, proof      128
Talagrand’s isoperimetric, inequality, proof      128
Talagrand’s isoperimetric, theorem      120
Talagrand’s isoperimetric, theory      119
Terada, R.      41
Terada, R.      41
Traveling-salesman problem, (TSP)      27
Traveling-salesman problem, (TSP)      27
Traveling-salesman problem, Gaussian tail bound      124
TSP means      67
TSP means for the minimal matching      70
TSP means for the MST      70
TSP means for the TSP      68
TSP means, basic theorem      54
TSP means, geometric from simple      64
TSP means, Redmond, C.      68
TSP means, refinements      21
TSP means, Renyi, A.      116
TSP means, Rhee, W. T.      14 24 33 38 59 65 72 75 124
TSP means, Richardson, D.      76
TSP means, Rinnooy Kan, A. H. G.      93
TSP means, Rinnooy Kan, A. H. G.      93
TSP means, Rinnot, Y.      112
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