This book covers the dominant theoretical approaches to the approximate solution of hard combinatorial optimization and enumeration problems. It contains elegant combinatorial theory, useful and interesting algorithms, and deep results about the intrinsic complexity of combinatorial problems. Its clarity of exposition and excellent selection of exercises will make it accessible and appealing to all those with a taste for mathematics and algorithms. Richard Karp,University Professor, University of California at Berkeley Following the development of basic combinatorial optimization techniques in the 1960s and 1970s, a main open question was to develop a theory of approximation algorithms. In the 1990s, parallel developments in techniques for designing approximation algorithms as well as methods for proving hardness of approximation results have led to a beautiful theory. The need to solve truly large instances of computationally hard problems, such as those arising from the Internet or the human genome project, has also increased interest in this theory. The field is currently very active, with the toolbox of approximation algorithm design techniques getting always richer. It is a pleasure to recommend Vijay Vazirani's well-written and comprehensive book on this important and timely topic. I am sure the reader will find it most useful both as an introduction to approximability as well as a reference to the many aspects of approximation algorithms. László Lovász, Senior Researcher, Microsoft Research

This monograph deals with designing polynomial time approximation algorithms for NP-hard combinatorial optimization problems. Although NP-complete problems do not offer footholds to find optimal solutions efficiently, they offer footholds to find near-optimal solutions efficiently. Designing polynomial time algorithms involves finding these footholds and exploiting them. The book discusses a wide range of combinatorial and LP-based algorithms in detail.

"Approximation algorithms are currently a central and fast-developing area of research in theoretical computer science. This monograph covers the basic techniques used in the latest research work, techniques that everyone in the field should know, and shows that they form the beginnings of a promising theory. The author consolidates progress made so far, including some very recent results, and makes a strong effort to convey the beauty and excitement of work in the field."

Includes bibliographical references (p. [355]-370) and index.

Introduction.- I. Combinatorial Algorithms: Set cover. Steiner tree and TSP. Multiway cuts and k-cuts. k-center. Feedback vertex set. Shortest superstring. Knapsack. Bin packing. Minimum makespan scheduling. Euclidean TSP.- II. LP-Based Algorithms: Introduction to LP-duality. Rounding applied to set cover. LP-duality based analysis for set cover. The primal-dual schema. Maximum satisfiability. Scheduling on unrelated parallel machines. Multicut and integer multicommodity flow in trees. Multiway cut. Multicut in general graphs. Sparsest cut. Steiner forest. Steiner network. Facility location. k-median. Semidefinite programming.- III. Other Topics: Counting problems. Shortest vector. Hardness of approximation. Open problems.