The design of approximation algorithms /

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Bibliographic Details
Author / Creator:	Williamson, David P.
Imprint:	New York : Cambridge University Press, 2011.
Description:	xi, 504 p. : ill. ; 26 cm.
Language:	English
Subject:	Approximation theory. Mathematical optimization. Approximation theory. Mathematical optimization.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/8391831

Hidden Bibliographic Details
Other authors / contributors:	Shmoys, David Bernard.
ISBN:	9780521195270 (hardback) 0521195276 (hardback)
Notes:	Includes bibliographical references and indexes.
Summary:	"Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems"--

Table of Contents:

Preface
I. An Introduction to the Techniques
1. An Introduction to Approximation Algorithms
1.1. The Whats and Whys of Approximation Algorithms
1.2. An Introduction to the Techniques and to Linear Programming: The Set Cover Problem
1.3. A Deterministic Rounding Algorithm
1.4. Rounding a Dual Solution
1.5. Constructing a Dual Solution: The Primal-Dual Method
1.7. A Randomized Rounding Algorithm
Exercises
Chapter Notes
2. Greedy Algorithms and Local Search
2.1. Scheduling Jobs with Deadlines on a Single Machine
2.2. The k-Center Problem
2.3. Scheduling Jobs on Identical Parallel Machines
2.4. The Traveling Salesman Problem
2.5. Maximizing Float in Bank Accounts
2.6. Finding Minimum-Degree Spanning Trees
2.7. Edge Coloring
Exercises
Chapter Notes
3. Rounding Data and Dynamic Programming
3.1. The Knapsack Problem
3.2. Scheduling Jobs on Identical Parallel Machines
3.3. The Bin-Packing Problem
Exercises
Chapter Notes
4. Deterministic Rounding of Linear Programs
4.1. Minimizing the Sum of Completion Times on a Single Machine
4.2. Minimizing the Weighted Sum of Completion Times on a Single Machine
4.3. Solving Large Linear Programs in Polynomial Time via the Ellipsoid Method
4.4. The Prize-Collecting Steiner Tree Problem
4.5. The Uncapacitated Facility Location Problem
4.6. The Bin-Packing Problem
Exercises
Chapter Notes
5. Random Sampling and Randomized Rounding of Linear Programs
5.1. Simple Algorithms for MAX SAT and MAX CUT
5.2. Derandomization
5.3. Flipping Biased Coins
5.4. Randomized Rounding
5.5. Choosing the Better of Two Solutions
5.6. Nonlinear Randomized Rounding
5.7. The Prize-Collecting Steiner Tree Problem
5.8. The Uncapacitated Facility Location Problem
5.9. Scheduling a Single Machine with Release Dates
5.10. Chernoff Bounds
5.11. Integer Multicommodity Flows
5.12. Random Sampling and Coloring Dense 3-Colorable Graphs
Exercises
Chapter Notes
6. Randomized Rounding of Semidefinite Programs
6.1. A Brief Introduction to Semidefinite Programming
6.2. Finding Large Cuts
6.3. Approximating Quadratic Programs
6.4. Finding a Correlation Clustering
6.5. Coloring 3-Colorable Graphs
Exercises
Chapter Notes
7. The Primal-Dual Method
7.1. The Set Cover Problem: A Review
7.2. Choosing Variables to Increase: The Feedback Vertex Set Problem in Undirected Graphs
7.3. Cleaning Up the Primal Solution: The Shortest s-t Path Problem
7.4. Increasing Multiple Variables at Once: The Generalized Steiner Tree Problem
7.5. Strengthening Inequalities: The Minimum Knapsack Problem
7.6. The Uncapacitated Facility Location Problem
7.7. Lagrangean Relaxation and the k-Median Problem
Exercises
Chapter Notes
8. Cuts and Metrics
8.1. The Multiway Cut Problem and a Minimum-Cut-Based Algorithm
8.2. The Multiway Cut Problem and an LP Rounding Algorithm
8.3. The Multicut Problem
8.4. Balanced Cuts
8.5. Probabilistic Approximation of Metrics by Tree Metrics
8.6. An Application of Tree Metrics: Buy-at-Bulk Network Design
8.7. Spreading Metrics, Tree Metrics, and Linear Arrangement
Exercises
Chapter Notes
II. Further Uses of the Techniques
9. Further Uses of Greedy and Local Search Algorithms
9.1. A Local Search Algorithm for the Uncapacitated Facility Location Problem
9.2. A Local Search Algorithm for the k-Median Problem
9.3. Minimum-Degree Spanning Trees
9.4. A Greedy Algorithm for the Uncapacitated Facility Location Problem
Exercises
Chapter Notes
10. Further Uses of Rounding Data and Dynamic Programming
10.1. The Euclidean Traveling Salesman Problem
10.2. The Maximum Independent Set Problem in Planar Graphs
Exercises
Chapter Notes
11. Further Uses of Deterministic Rounding of Linear Programs
11.1. The Generalized Assignment Problem
11.2. Minimum-Cost Bounded-Degree Spanning Trees
11.3. Survivable Network Design and Iterated Rounding
Exercises
Chapter Notes
12. Further Uses of Random Sampling and Randomized Rounding of Linear Programs
12.1. The Uncapacitated Facility Location Problem
12.2. The Single-Source Rent-or-Buy Problem
12.3. The Steiner Tree Problem
12.4. Everything at Once: Finding a Large Cut in a Dense Graph
Exercises
Chapter Notes
13. Further Uses of Randomized Rounding of Semidefinite Programs
13.1. Approximating Quadratic Programs
13.2. Coloring 3-Colorable Graphs
13.3. Unique Games
Exercises
Chapter Notes
14. Further Uses of the Primal-Dual Method
14.1. The Prize-Collecting Steiner Tree Problem
14.2. The Feedback Vertex Set Problem in Undirected Graphs
Exercises
Chapter Notes
15. Further Uses of Cuts and Metrics
15.1. Low-Distortion Embeddings and the Sparsest Cut Problem
15.2. Oblivious Routing and Cut-Tree Packings
15.3. Cut-Tree Packings and the Minimum Bisection Problem
15.4. The Uniform Sparsest Cut Problem
Exercises
Chapter Notes
16. Techniques in Proving the Hardness of Approximation
16.1. Reductions from NP-Complete Problems
16.2. Reductions that Preserve Approximation
16.3. Reductions from Probabilistically Checkable Proofs
16.4. Reductions from Label Cover
16.5. Reductions from Unique Games
Chapter Notes
17. Open Problems
Appendix A. Linear Programming
Appendix B. NP-Completeness
Bibliography
Author Index
Subject Index

The design of approximation algorithms /

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