© 1999

Handbook of Combinatorial Optimization

Supplement Volume A

  • Ding-Zhu Du
  • Panos M. Pardalos

Table of contents

  1. Front Matter
    Pages i-viii
  2. Immanuel M. Bomze, Marco Budinich, Panos M. Pardalos, Marcello Pelillo
    Pages 1-74
  3. Rainer E. Burkard, Eranda Çela
    Pages 75-149
  4. Edward G. Coffman, Gabor Galambos, Silvano Martello, Daniele Vigo
    Pages 151-207
  5. Paola Festa, Panos M. Pardalos, Mauricio G. C. Resende
    Pages 209-258
  6. Theodore B. Trafalis, Suat Kasap
    Pages 259-293
  7. Robert A. Murphey, Panos M. Pardalos, Mauricio G. C. Resende
    Pages 295-377
  8. Jun Gu, Paul W. Purdom, John Franco, Benjamin W. Wah
    Pages 379-572
  9. Jens Albrecht, Dietmar Cieslik
    Pages 573-589
  10. Wenqi Huang, Yu-Liang Wu, C. K. Wong
    Pages 591-605
  11. Back Matter
    Pages 607-648

About this book


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).


Analysis algorithms combinatorial optimization linear optimization optimization

Editors and affiliations

  • Ding-Zhu Du
    • 1
    • 2
  • Panos M. Pardalos
    • 3
  1. 1.Department of Computer ScienceUniversity of MinnesotaUSA
  2. 2.Institute of Applied MathematicsAcademia SinicaP. R. China
  3. 3.Department of Industrial and Systems EngineeringUniversity of FloridaUSA

Bibliographic information

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