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Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully written as teaching aids and highlight characteristic features of the theory. Although these books are frequently used as textbooks in graduate courses, they are also suitable for individual study. 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher's location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) PrefaceInteger programming is a thriving area of optimization, which is applied nowadays to a multitude of human endeavors, thanks to high quality software. It was developed over several decades and is still evolving rapidly.The goal of this book is to present the mathematical foundations of integer programming, with emphasis on the techniques that are most successful in current software implementations: convexification and enumeration.This textbook is intended for a graduate course in integer programming in M.S. or Ph.D. programs in applied mathematics, operations research, industrial engineering, or computer science.To better understand the excitement that is generated today by this area of mathematics, it is helpful to provide a historical perspective.Babylonian tablets show that mathematicians were already solving systems of lin...

A graph is Berge if no induced subgraph of G is an odd cycle of length at least five or the complement of one. In this paper we give an algorithm to test if a graph G is Berge, with running time O(|V (G)| 9 ). This is independent of the recent proof of the strong perfect graph conjecture. (2000): 05C17 Mathematics Subject Classification

this document has bien oapprov-ed for public release and sale; its distribution is unhimited.This research was supported in part by the National Science Foundation, Grant #DDM-8901495 and the Office of Naval Research through Contract N00014-85-K-0198. Management Science Research Group Graduate School of Industrial AdministrationCarnegie Mellon University Pittsburgh, PA 15213 AbstractWe propose a cutting plane algorithm for mixed 0-1 programs based on a family of polyhedra which strengthen the usual LP relaxation. We show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point. This cut is found through the solution of a linear program that has about twice the size of the usual LP relaxation. A lifting step is used to reduce the size of the LP's needed to generate the cuts. An additional strengthening step suggested by Baas and Jeroslow is then applied. We report our computational experience with a preliminary version of the algorithm. This approach is related to the work of Balas on disjunctive programming, the matrix cut relaxations of Lovisz and Schrijver and the hierarchy of relaxations of Sherali and Adams.