- Page 4 and 5: 2This electronic-only manuscript is
- Page 8 and 9: 6 PrefaceElectronic web edition. Co
- Page 10 and 11: 8 Table of Contents4.3 Solving larg
- Page 12 and 13: 10 Table of ContentsB NP-completene
- 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
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- 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
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- Page 45 and 46: 2.4 The traveling salesman problem
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- Page 49 and 50: 2.5 Maximizing float in bank accoun
- Page 51 and 52: 2.6 Finding minimum-degree spanning
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2.7 Edge coloring 553-edge-colorabl
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2.7 Edge coloring 57uuv 0 v 2 v 3 v
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2.7 Edge coloring 592.2 Prove Lemma
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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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4.5 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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5.8 The uncapacitated facility loca
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5.8 The uncapacitated facility loca
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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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5.12 Random sampling and coloring d
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5.12 Random sampling and coloring d
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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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6.5 Coloring 3-colorable graphs 155
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6.5 Coloring 3-colorable graphs 157
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6.5 Coloring 3-colorable graphs 159
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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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7.4 Increasing multiple variables a
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7.4 Increasing multiple variables a
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7.4 Increasing multiple variables a
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7.5 Strengthening inequalities: the
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7.6 The uncapacitated facility loca
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7.6 The uncapacitated facility loca
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7.7 Lagrangean relaxation and the k
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7.7 Lagrangean relaxation and the k
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7.7 Lagrangean relaxation and the k
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7.7 Lagrangean relaxation and the k
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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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8.2 The multiway cut problem and an
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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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8.5 Probabilistic approximation of
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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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8.7 Spreading metrics, tree metrics
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8.7 Spreading metrics, tree metrics
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8.7 Spreading metrics, 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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236 Further uses of greedy and loca
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238 Further uses of greedy and loca
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240 Further uses of greedy and loca
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242 Further uses of greedy and loca
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244 Further uses of greedy and loca
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246 Further uses of greedy and loca
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248 Further uses of greedy and loca
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250 Further uses of greedy and loca
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252 Further uses of greedy and loca
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254 Further uses of greedy and loca
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256 Further uses of greedy and loca
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258 Further uses of rounding data a
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260 Further uses of rounding data a
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262 Further uses of rounding data a
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264 Further uses of rounding data a
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266 Further uses of rounding data a
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268 Further uses of rounding data a
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270 Further uses of rounding data a
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272 Further uses of rounding data a
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274 Further uses of rounding data a
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276 Further uses of rounding data a
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278 Further uses of rounding data a
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280 Further uses of rounding data a
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282 Further uses of deterministic r
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284 Further uses of deterministic r
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286 Further uses of deterministic r
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288 Further uses of deterministic r
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290 Further uses of deterministic r
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292 Further uses of deterministic r
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294 Further uses of deterministic r
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296 Further uses of deterministic r
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298 Further uses of deterministic r
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300 Further uses of deterministic r
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302 Further uses of deterministic r
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304 Further uses of deterministic r
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306 Further uses of deterministic r
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308 Further uses of deterministic r
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310 Further uses of random sampling
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312 Further uses of random sampling
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314 Further uses of random sampling
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316 Further uses of random sampling
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318 Further uses of random sampling
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320 Further uses of random sampling
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322 Further uses of random sampling
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324 Further uses of random sampling
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326 Further uses of random sampling
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328 Further uses of random sampling
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330 Further uses of random sampling
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332 Further uses of random sampling
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334 Further uses of randomized roun
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336 Further uses of randomized roun
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338 Further uses of randomized roun
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340 Further uses of randomized roun
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342 Further uses of randomized roun
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344 Further uses of randomized roun
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346 Further uses of randomized roun
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348 Further uses of randomized roun
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350 Further uses of randomized roun
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352 Further uses of randomized roun
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354 Further uses of randomized roun
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356 Further uses of the primal-dual
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358 Further uses of the primal-dual
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360 Further uses of the primal-dual
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362 Further uses of the primal-dual
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364 Further uses of the primal-dual
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366 Further uses of the primal-dual
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368 Further uses of the primal-dual
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370 Further uses of cuts and metric
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372 Further uses of cuts and metric
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374 Further uses of cuts and metric
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376 Further uses of cuts and metric
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378 Further uses of cuts and metric
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380 Further uses of cuts and metric
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382 Further uses of cuts and metric
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384 Further uses of cuts and metric
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386 Further uses of cuts and metric
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388 Further uses of cuts and metric
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390 Further uses of cuts and metric
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392 Further uses of cuts and metric
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394 Further uses of cuts and metric
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396 Further uses of cuts and metric
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398 Further uses of cuts and metric
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400 Further uses of cuts and metric
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402 Further uses of cuts and metric
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404 Further uses of cuts and metric
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406 Further uses of cuts and metric
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408 Techniques in proving the hardn
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410 Techniques in proving the hardn
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412 Techniques in proving the hardn
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414 Techniques in proving the hardn
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416 Techniques in proving the hardn
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418 Techniques in proving the hardn
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420 Techniques in proving the hardn
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422 Techniques in proving the hardn
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424 Techniques in proving the hardn
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426 Techniques in proving the hardn
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428 Techniques in proving the hardn
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430 Techniques in proving the hardn
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432 Techniques in proving the hardn
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434 Techniques in proving the hardn
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436 Techniques in proving the hardn
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438 Techniques in proving the hardn
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440 Techniques in proving the hardn
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442 Techniques in proving the hardn
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444 Techniques in proving the hardn
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446 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