Handbook of Combinatorial Optimization

Volume1–3

  • Ding-Zhu Du
  • Panos M. Pardalos

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. C. S. Adjiman, C. A. Schweiger, C. A. Floudas
    Pages 1-76
  3. Roberto Battiti, Marco Protasi
    Pages 77-148
  4. Franco Giannessi, Fabio Tardella
    Pages 149-188
  5. John E. Mitchell, Panos M. Pardalos, Mauricio G. C. Resende
    Pages 189-297
  6. David Pisinger, Paolo Toth
    Pages 299-428
  7. Tomasz Radzik
    Pages 429-478
  8. Hanif D. Sherali, Warren P. Adams
    Pages 479-532
  9. Rekha R. Thomas
    Pages 533-572
  10. Bhaskar DasGupta, Xin He, Tao Jiang, Ming Li, John Tromp, Lusheng Wang et al.
    Pages 781-822
  11. Naoki Katoh, Toshihide Ibaraki
    Pages 905-1006
  12. Boris Mirkin, Ilya Muchnik
    Pages 1007-1075
  13. Panos M. Pardalos, Thelma Mavridou, Jue Xue
    Pages 1077-1141
  14. Jens Starke, Michael Schanz
    Pages 1217-1270
  15. Wen-Guey Tzeng
    Pages 1271-1288

About this book

Introduction

Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math­ ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air­ line crew scheduling, corporate planning, computer-aided design and man­ ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca­ tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover­ ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo­ rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi­ tion, linear programming relaxations are often the basis for many approxi­ mation algorithms for solving NP-hard problems (e.g. dual heuristics).

Keywords

algorithms artificial intelligence combinatorial optimization communication dynamical systems graph theory heuristics linear optimization network nonlinear optimization number theory operations research optimization programming statistics

Editors and affiliations

  • Ding-Zhu Du
    • 1
  • Panos M. Pardalos
    • 2
  1. 1.University of MinnesotaMinneapolisUSA
  2. 2.University of FloridaGainesvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0303-9
  • Copyright Information Springer-Verlag US 1999
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-7987-4
  • Online ISBN 978-1-4613-0303-9
  • About this book