Combinatorial Optimization Theory and Algorithms
This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and
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Bernhard Korte Jens Vygen
Combinatorial Optimization Theory and Algorithms Sixth Edition
Algorithms and Combinatorics Volume 21
Editorial Board William J. Cook Ronald Graham Bernhard Korte László Lovász Avi Wigderson Günter M. Ziegler
More information about this series at http://www.springer.com/series/13
Bernhard Korte • Jens Vygen
Combinatorial Optimization Theory and Algorithms Sixth Edition
123
Bernhard Korte Research Institute for Discrete Mathematics University of Bonn Bonn, Germany
Jens Vygen Research Institute for Discrete Mathematics University of Bonn Bonn, Germany
ISSN 0937-5511 ISSN 2197-6783 (electronic) Algorithms and Combinatorics ISBN 978-3-662-56038-9 ISBN 978-3-662-56039-6 (eBook) https://doi.org/10.1007/978-3-662-56039-6 Library of Congress Control Number: 2017958030 Mathematics Subject Classification (2010): 90C27, 68R10, 05C85, 68Q25 © Springer-Verlag GmbH Germany 2000, 2002, 2006, 2008, 2012, 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer-Verlag GmbH, DE The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany
Preface to the Sixth Edition
After six years, it was again time for a new edition. Besides updates, new exercises, and a few corrections, it contains the following new material. Section 7.4 is devoted to shallow-light trees. Section 14.6 contains the recent two-factor approximation algorithm for submodular function maximization. Section 17.5 discusses the Nemhauser-Ullmann algorithm and smoothed analysis. In Section 20.3, we present the (ln 4 + )-factor approximation algorithm for the Steiner tree problem. Finally, Section 20.7 contains the VPN theorem. There are also small additions, e.g. on the integrality ratio in Section 5.1 and kernelization in Section 15.7. We would l
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