Design of Approximation Algorithms

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10 Table <strong>of</strong> ContentsB NP-completeness 457Bibliography 461Author index 481Electronic web edition. Copyright 2011 by David P. Williamson and David B. Shmoys.To be published by Cambridge University Press
Part IAn introduction to the techniques11
Page 4 and 5: 2This electronic-only manuscript is
Page 6 and 7: 4 Prefacelems in database and progr
Page 8 and 9: 6 PrefaceElectronic web edition. Co
Page 10 and 11: 8 Table of Contents4.3 Solving larg
Page 15 and 16: C h a p t e r 1An introduction to a
Page 17 and 18: 1.1 The whats and whys of approxima
Page 19 and 20: 1.2 An introduction to the techniqu
Page 21 and 22: 1.3 A deterministic rounding algori
Page 23 and 24: 1.4 Rounding a dual solution 21This
Page 25 and 26: 1.5 Constructing a dual solution: t
Page 27 and 28: 1.6 A greedy algorithm 25I ← ∅
Page 29 and 30: 1.6 A greedy algorithm 27To constru
Page 31 and 32: 1.7 A randomized rounding algorithm
Page 37 and 38: C h a p t e r 2Greedy algorithms an
Page 39 and 40: 2.2 The k-center problem 37Let L
Page 41 and 42: 2.3 Scheduling jobs on identical pa
Page 43 and 44: 2.3 Scheduling jobs on identical pa
Page 45 and 46: 2.4 The traveling salesman problem
Page 47 and 48: 2.4 The traveling salesman problem
Page 49 and 50: 2.5 Maximizing float in bank accoun
Page 51 and 52: 2.6 Finding minimum-degree spanning
Page 57 and 58: 2.7 Edge coloring 553-edge-colorabl
Page 59 and 60: 2.7 Edge coloring 57uuv 0 v 2 v 3 v
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2.7 Edge coloring 612.12 A matroid
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2.7 Edge coloring 63a minimum-degre
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C h a p t e r 3Rounding data and dy
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3.1 The knapsack problem 67{(0, 0),
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3.2 Scheduling jobs on identical pa
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3.2 Scheduling jobs on identical pa
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3.3 The bin-packing problem 733.3 T
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3.3 The bin-packing problem 75tryin
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3.3 The bin-packing problem 77input
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3.3 The bin-packing problem 79Gens
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C h a p t e r 4Deterministic roundi
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4.1 Minimizing the sum of completio
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4.2 Minimizing the weighted sum of
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4.3 Solving large linear programs i
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4.4 The prize-collecting Steiner tr
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4.5 The uncapacitated facility loca
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4.6 The bin-packing problem 95Solve
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4.6 The bin-packing problem 97and a
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4.6 The bin-packing problem 99BinPa
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4.6 The bin-packing problem 101Exer
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4.6 The bin-packing problem 103(b)
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C h a p t e r 5Random sampling and
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5.1 Simple algorithms for MAX SAT a
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5.2 Derandomization 109Assuming for
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5.4 Randomized rounding 111Proof. L
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5.4 Randomized rounding 113a+ba0 1F
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5.5 Choosing the better of two solu
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5.6 Non-linear randomized rounding
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5.7 The prize-collecting Steiner tr
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5.9 Scheduling a single machine wit
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5.9 Scheduling a single machine wit
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5.10 Chernoff bounds 129The second
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5.10 Chernoff bounds 131for 0 ≤
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5.12 Random sampling and coloring d
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C h a p t e r 6Randomized rounding
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6.2 Finding large cuts 1436.2 Findi
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6.2 Finding large cuts 145ABv jθO
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6.3 Approximating quadratic program
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6.3 Approximating quadratic program
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6.4 Finding a correlation clusterin
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6.5 Coloring 3-colorable graphs 153
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C h a p t e r 7The primal-dual meth
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7.1 The set cover problem: a review
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7.2 Choosing variables to increase:
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7.2 Choosing variables to increase:
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7.3 Cleaning up the primal solution
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7.4 Increasing multiple variables a
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7.5 Strengthening inequalities: the
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7.7 Lagrangean relaxation and the k
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C h a p t e r 8Cuts and metricsIn t
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8.2 The multiway cut problem and an
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8.3 The multicut problem 2038.3 The
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8.3 The multicut problem 2051/4s i1
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8.3 The multicut problem 207Observe
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8.4 Balanced cuts 209paths between
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8.5 Probabilistic approximation of
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8.6 An application of tree metrics:
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8.6 An application of tree metrics:
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8.7 Spreading metrics, tree metrics
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Part IIFurther uses of the techniqu
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234 Further uses of greedy and loca
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258 Further uses of rounding data a
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282 Further uses of deterministic r
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310 Further uses of random sampling
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334 Further uses of randomized roun
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356 Further uses of the primal-dual
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370 Further uses of cuts and metric
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408 Techniques in proving the hardn
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448 Open ProblemskFigure 17.1: Illu
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450 Open Problemsbeen settled via a
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452 Open ProblemsElectronic web edi
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454 Linear programmingrequire that
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456 Linear programmingCorollary A.3
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458 NP-completenessof “short proo
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460 NP-completenessFor example, the
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462 Bibliography[11] S. Arora. Poly
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464 Bibliography[43] M. Bellare, S.
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466 Bibliography[74] F. A. Chudak,
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468 Bibliography[109] U. Feige and
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470 Bibliography[140] M. X. Goemans
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472 Bibliography[172] W.-L. Hsu and
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474 Bibliography[204] G. Kortsarz,
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476 Bibliography[235] Y. Nesterov.
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478 Bibliography[270] W. E. Smith.
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480 BibliographyElectronic web edit
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482 Author indexCormen, T. H. 33Cor
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484 Author indexPlaxton, C. G. 254,
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IndexΦ (cumulative distribution fu
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488 INDEXdemand graph, 352dense gra
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490 INDEXHamiltonian path, 50, 60ha
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492 INDEXfor generalized Steiner tr
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494 INDEXdistortion, 212, 370-371,
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496 INDEXrandomized rounding algori
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498 INDEXlinear programming relaxat
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500 INDEXweakly NP-complete, 459wea
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Design of Approximation Algorithms

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