Handbook of Combinatorial Optimization

1. Front Matter

   Pages i-viii

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2. The Maximum Clique Problem

   • Immanuel M. Bomze, Marco Budinich, Panos M. Pardalos, Marcello Pelillo

   Pages 1-74

3. Linear Assignment Problems and Extensions

   • Rainer E. Burkard, Eranda Çela

   Pages 75-149

4. Bin Packing Approximation Algorithms: Combinatorial Analysis

   • Edward G. Coffman, Gabor Galambos, Silvano Martello, Daniele Vigo

   Pages 151-207

5. Feedback Set Problems

   • Paola Festa, Panos M. Pardalos, Mauricio G. C. Resende

   Pages 209-258

6. Neural Networks Approaches for Combinatorial Optimization Problems

   • Theodore B. Trafalis, Suat Kasap

   Pages 259-293

7. Frequency Assignment Problems

   • Robert A. Murphey, Panos M. Pardalos, Mauricio G. C. Resende

   Pages 295-377

8. Algorithms for the Satisfiability (SAT) Problem

   • Jun Gu, Paul W. Purdom, John Franco, Benjamin W. Wah

   Pages 379-572

9. The Steiner Ratio of L _p -planes

   • Jens Albrecht, Dietmar Cieslik

   Pages 573-589

10. A Cogitative Algorithm for Solving the Equal Circles Packing Problem

    • Wenqi Huang, Yu-Liang Wu, C. K. Wong

    Pages 591-605

11. Back Matter

    Pages 607-648

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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. dualheuristics).

• Analysis
• algorithms
• combinatorial optimization
• linear optimization
• optimization
• combinatorics
• information and communication, circuits

• Department of Computer Science, University of Minnesota, USA

  Ding-Zhu Du

• Institute of Applied Mathematics, Academia Sinica, P. R. China

  Ding-Zhu Du

• Department of Industrial and Systems Engineering, University of Florida, USA

  Panos M. Pardalos

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