Approximation algorithms Approximation algorithms Image
AUTEUR Vijay-V Vazirani
ISBN 9783540653677
The field of approximation algorithms, perhaps the most active area of algorithmic research today, combines a rich and deep mathematical theory with the promise of profound practical impact. Most computational problems arising across a very broad spectrum of application areas, such as VLSI design, design and operation of networks, web-related problems, scheduling, manufacturing, game theory, biology, and number theory, are NP-hard, hence making their exact solution prohibitively time-consuming. This challenge has motivated the growth of an impressive literature, providing approximation algorithms for this very diverse collection of problems. A slew of spectacular results in the last decade has revolutionized the field. The challenge met by this book is to capture the beauty and excitement of work in this thriving field and to convey in a lucid manner the underlying theory and methodology. Many of the research results presented have been simplified, and new insights provided Perhaps the most important aspect of the book is that it shows simple ways of talking about complex, powerful algorithmic ideas by giving intuitive proofs, by writing algorithms in plain English, and by providing numerous critical examples and illustrations. This book will be of interest to the scientific community at large and, in particular, to students and researchers in Computer Science, Operations Research, and Discrete Mathematics. It can be used both as a text in a graduate course on approximation algorithms and as a supplementary text in basic undergraduate and graduate courses on algorithms.
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Approximation algorithms as a research area is closely related to and informed by inapproximability theory where the non-existence of efficient algorithms with certain approximation ratios is proved (conditioned on widely believed hypotheses such as the P ≠ NP conjecture) by means of reductions.

Thus, the algorithm is quartically convergent, which means that the number of correct digits of the approximation roughly quadruples with each iteration. The original presentation, using modern notation, is as follows: To calculate S {\displaystyle {\sqrt {S}}} , let x 0 2 be the initial approximation to S .

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