Design of Approximation Algorithms

ISBN-10: 0521195276
ISBN-13: 9780521195270
Edition: 2011
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Book details

List price: $67.95
Copyright year: 2011
Publisher: Cambridge University Press
Publication date: 4/26/2011
Binding: Hardcover
Pages: 516
Size: 7.50" wide x 10.50" long x 1.25" tall
Weight: 2.332
Language: English

David P. Williamson is a Professor at Cornell University with a joint appointment in the School of Operations Research and Information Engineering and in the Department of Information Science. Prior to joining Cornell, he was a Research Staff Member at the IBM T.J. Watson Research Center and a Senior Manager at the IBM Almaden Research Center. He has won several awards for his work on approximation algorithms, including the 2000 Fulkerson Prize, sponsored by the American Mathematical Society and the Mathematical Programming Society. He has served on several editorial boards, including ACM Transactions on Algorithms, Mathematics of Operations Research, the SIAM Journal on Computing, and the SIAM Journal on Discrete Mathematics.

David Shmoys has faculty appointments in both the School of Operations Research and Information Engineering and the Department of Computer Science, and he is currently Associate Director of the Institute for Computational Sustainability at Cornell University. He is a Fellow of the ACM, was an NSF Presidential Young Investigator, and has served on numerous editorial boards, including Mathematics of Operations Research (for which he is currently an associate editor), Operations Research, ORSA Journal on Computing, Mathematical Programming, and both the SIAM Journal of Computing and Journal of Discrete Mathematics; he also served as editor-in-chief for the latter.

Preface
An Introduction to the Techniques
An Introduction to Approximation Algorithms
The Whats and Whys of Approximation Algorithms
An Introduction to the Techniques and to Linear Programming: The Set Cover Problem
A Deterministic Rounding Algorithm
Rounding a Dual Solution
Constructing a Dual Solution: The Primal-Dual Method
A Randomized Rounding Algorithm
Exercises
Chapter Notes
Greedy Algorithms and Local Search
Scheduling Jobs with Deadlines on a Single Machine
The k-Center Problem
Scheduling Jobs on Identical Parallel Machines
The Traveling Salesman Problem
Maximizing Float in Bank Accounts
Finding Minimum-Degree Spanning Trees
Edge Coloring
Exercises
Chapter Notes
Rounding Data and Dynamic Programming
The Knapsack Problem
Scheduling Jobs on Identical Parallel Machines
The Bin-Packing Problem
Exercises
Chapter Notes
Deterministic Rounding of Linear Programs
Minimizing the Sum of Completion Times on a Single Machine
Minimizing the Weighted Sum of Completion Times on a Single Machine
Solving Large Linear Programs in Polynomial Time via the Ellipsoid Method
The Prize-Collecting Steiner Tree Problem
The Uncapacitated Facility Location Problem
The Bin-Packing Problem
Exercises
Chapter Notes
Random Sampling and Randomized Rounding of Linear Programs
Simple Algorithms for MAX SAT and MAX CUT
Derandomization
Flipping Biased Coins
Randomized Rounding
Choosing the Better of Two Solutions
Nonlinear Randomized Rounding
The Prize-Collecting Steiner Tree Problem
The Uncapacitated Facility Location Problem
Scheduling a Single Machine with Release Dates
Chernoff Bounds
Integer Multicommodity Flows
Random Sampling and Coloring Dense 3-Colorable Graphs
Exercises
Chapter Notes
Randomized Rounding of Semidefinite Programs
A Brief Introduction to Semidefinite Programming
Finding Large Cuts
Approximating Quadratic Programs
Finding a Correlation Clustering
Coloring 3-Colorable Graphs
Exercises
Chapter Notes
The Primal-Dual Method
The Set Cover Problem: A Review
Choosing Variables to Increase: The Feedback Vertex Set Problem in Undirected Graphs
Cleaning Up the Primal Solution: The Shortest s-t Path Problem
Increasing Multiple Variables at Once: The Generalized Steiner Tree Problem
Strengthening Inequalities: The Minimum Knapsack Problem
The Uncapacitated Facility Location Problem
Lagrangean Relaxation and the k-Median Problem
Exercises
Chapter Notes
Cuts and Metrics
The Multiway Cut Problem and a Minimum-Cut-Based Algorithm
The Multiway Cut Problem and an LP Rounding Algorithm
The Multicut Problem
Balanced Cuts
Probabilistic Approximation of Metrics by Tree Metrics
An Application of Tree Metrics: Buy-at-Bulk Network Design
Spreading Metrics, Tree Metrics, and Linear Arrangement
Exercises
Chapter Notes
Further Uses of the Techniques
Further Uses of Greedy and Local Search Algorithms
A Local Search Algorithm for the Uncapacitated Facility Location Problem
A Local Search Algorithm for the k-Median Problem
Minimum-Degree Spanning Trees
A Greedy Algorithm for the Uncapacitated Facility Location Problem
Exercises
Chapter Notes
Further Uses of Rounding Data and Dynamic Programming
The Euclidean Traveling Salesman Problem
The Maximum Independent Set Problem in Planar Graphs
Exercises
Chapter Notes
Further Uses of Deterministic Rounding of Linear Programs
The Generalized Assignment Problem
Minimum-Cost Bounded-Degree Spanning Trees
Survivable Network Design and Iterated Rounding
Exercises
Chapter Notes
Further Uses of Random Sampling and Randomized Rounding of Linear Programs
The Uncapacitated Facility Location Problem
The Single-Source Rent-or-Buy Problem
The Steiner Tree Problem
Everything at Once: Finding a Large Cut in a Dense Graph
Exercises
Chapter Notes
Further Uses of Randomized Rounding of Semidefinite Programs
Approximating Quadratic Programs
Coloring 3-Colorable Graphs
Unique Games
Exercises
Chapter Notes
Further Uses of the Primal-Dual Method
The Prize-Collecting Steiner Tree Problem
The Feedback Vertex Set Problem in Undirected Graphs
Exercises
Chapter Notes
Further Uses of Cuts and Metrics
Low-Distortion Embeddings and the Sparsest Cut Problem
Oblivious Routing and Cut-Tree Packings
Cut-Tree Packings and the Minimum Bisection Problem
The Uniform Sparsest Cut Problem
Exercises
Chapter Notes
Techniques in Proving the Hardness of Approximation
Reductions from NP-Complete Problems
Reductions that Preserve Approximation
Reductions from Probabilistically Checkable Proofs
Reductions from Label Cover
Reductions from Unique Games
Chapter Notes
Open Problems
Linear Programming
NP-Completeness
Bibliography
Author Index
Subject Index

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