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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
The rich, multi-faceted and multi-disciplinary field of
matching-based market design is an active and important one due to
its highly successful applications with economic and sociological
impact. Its home is economics, but with intimate connections to
algorithm design and operations research. With chapters contributed
by over fifty top researchers from all three disciplines, this
volume is unique in its breadth and depth, while still being a
cohesive and unified picture of the field, suitable for the
uninitiated as well as the expert. It explains the dominant ideas
from computer science and economics underlying the most important
results on market design and introduces the main algorithmic
questions and combinatorial structures. Methodologies and
applications from both the pre-Internet and post-Internet eras are
covered in detail. Key chapters discuss the basic notions of
efficiency, fairness and incentives, and the way market design
seeks solutions guided by normative criteria borrowed from social
choice theory.
In recent years game theory has had a substantial impact on
computer science, especially on Internet- and e-commerce-related
issues. Algorithmic Game Theory, first published in 2007, develops
the central ideas and results of this exciting area in a clear and
succinct manner. More than 40 of the top researchers in this field
have written chapters that go from the foundations to the state of
the art. Basic chapters on algorithmic methods for equilibria,
mechanism design and combinatorial auctions are followed by
chapters on important game theory applications such as incentives
and pricing, cost sharing, information markets and cryptography and
security. This definitive work will set the tone of research for
the next few years and beyond. Students, researchers, and
practitioners alike need to learn more about these fascinating
theoretical developments and their widespread practical
application.
Covering the basic techniques used in the latest research work, the
author consolidates progress made so far, including some very
recent and promising results, and conveys the beauty and excitement
of work in the field. He gives clear, lucid explanations of key
results and ideas, with intuitive proofs, and provides critical
examples and numerous illustrations to help elucidate the
algorithms. Many of the results presented have been simplified and
new insights provided. Of interest to theoretical computer
scientists, operations researchers, and discrete mathematicians.
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