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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
David P Williamson; David Bernard Shmoys |

ISBN: | 9780521195270 0521195276 |

OCLC Number: | 671709856 |

Awards: | Winner of Lanchester Prize 2013 |

Description: | xi, 504 pages : illustrations ; 26 cm |

Contents: | Machine generated contents note: 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 -- 1.6. A Greedy Algorithm -- 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. |

Responsibility: | David P. Williamson, David B. Shmoys. |

More information: |

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## Reviews

*Editorial reviews*

Publisher Synopsis

"This is a beautifully written book that will bring anyone who reads it to the current frontiers of research in approximation algorithms. It covers everything from the classics to the latest, most exciting results such as ARV's sparsest cut algorithm, and does so in an extraordinarily clear, rigorous and intuitive manner." Anna Karlin, University of Washington "The authors of this book are leading experts in the area of approximation algorithms. They do a wonderful job in providing clear and unified explanations of subjects ranging from basic and fundamental algorithmic design techniques to advanced results in the forefront of current research. This book will be very valuable to students and researchers alike." Uriel Feige, Professor of Computer Science and Applied Mathematics, the Weizmann Institute "Theory of approximation algorithms is one of the most exciting areas in theoretical computer science and operations research. This book, written by two leading researchers, systematically covers all the important ideas needed to design effective approximation algorithms. The description is lucid, extensive and up-to-date. This will become a standard textbook in this area for graduate students and researchers." Toshihide Ibaraki, The Kyoto College of Graduate Studies for Informatics "This book on approximation algorithms is a beautiful example of an ideal textbook. It gives a concise treatment of the major techniques, results and references in approximation algorithms and provides an extensive and systematic coverage of this topic up to the frontier of current research. It will become a standard textbook and reference for graduate students, teachers and researchers in the field." Rolf H. Moehring, Technische Universitat Berlin "I have fond memories of learning approximation algorithms from an embryonic version of this book. The reader can expect a clearly written and thorough tour of all the important paradigms for designing efficient heuristics with provable performance guarantees for combinatorial optimization problems." Tim Roughgarden, Stanford University "This book is very well written. It could serve as a textbook on the design of approximation algorithms for discrete optimization problems. Readers will enjoy the clear and precise explanation of modern concepts, and the results obtained in this very elegant theory. Solving the exercises will benefit all readers interested in gaining a deeper understanding of the methods and results in the approximate algorithms for discrete optimization area." Alexander Kreinin, Computing Reviews "Any researcher interested in approximation algorithms would benefit greatly from this new book by Williamson and Schmoys. It is an ideal starting point for the fresh graduate student, as well as an excellent reference for the experts in the field. The wrting style is very clear and lucid, and it was a pleasure reading and reviewing this book." Deeparnab Chakrabarty for SIGACT News "The structure of the book is very interesting and allows a deeper understanding of the techniques presented. The whole book manages to develop a way of analyzing approximation algorithms and of designing approximation algorithms that perform well." Dana Simian, Mathematical Reviews Read more...

*User-contributed reviews*

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