基本説明
This second edition features 30% new additional content, additional chapters as well as updated content. The editors have brought together almost every aspect of this enormous field of combinatorial optimization, an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communications networks, and management science. An international team of 30-40 experts in the field form the editorial board.
Full Description
The second edition of this 5-volume handbook is intended to be a basic yet comprehensive reference work in combinatorial optimization that will benefit newcomers and researchers for years to come. This multi-volume work deals with several algorithmic approaches for discrete problems as well as with many combinatorial problems. The editors have brought together almost every aspect of this enormous field of combinatorial optimization, an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communications networks, and management science. An international team of 30-40 experts in the field form the editorial board.
The Handbook of Combinatorial Optimization, second edition is addressed to all scientists who use combinatorial optimization methods to model and solve problems. Experts in the field as well as non-specialists will find the material stimulating and useful.
Contents
Introduction.- Part 1. General Methodology.- Analysis of Greedy Approximations.- Guillotine Partition in Geometric Optimization.- Mixed-Integer Nonlinear Optimization in Process Synthesis.- Connection between Nonlinear Programming and Discrete Optimization.- Interior Point Methods for Combinatorial Optimization.- Fractional Combinatorial Optimization.- Reformulation-Linearization Techniques for Discrete Optimization Problems.- Grobner Bases in Integer Programming.- Dynamical System Approaches to Combinatorial Optimization.- Semidefinite Relaxation, Multivariate Norma Distribution and Order Statistics.- Selected Algorithmic Techniques for Parallel Optimization.- Multispace Search for Combinatorial Optimization.- Randomized Parallel Algorithms for Combinatorial Optimization.- Tabu Search.- Neural Network Approach for Combinatorial Optimization.- Data Correcting Algorithms in Combinatorial Optimization.- Probabilistic Verification and Non-Approximability.- Part 2. Classic Problems.- The Steiner ratio of $L_p$-planes.- The Maximum Clique Problem.- The Generalized Assignment Problem and Extension.- Linear Assignment Problems and Extensions.- Bin Packing Approximation Algorithms: Combinatorial Analysis.- Feedback Set Problems.- The Equitable Coloring of Graphs.- Approximate Algorithms and Heuristics for MAX-SAT.- Knapsack Problems.- Steiner Minimum Trees in E^3.- The Graph Coloring Problem: A Bibliographic Survey.- Steiner Minimum Trees: An Introduction, Parallel Computation, and Future Work.- Resource Allocation Problems.- Efficient Algorithms for Geometric Shortest Path Query Problem.- On-line Dominating Set Problems for Graphs.- Minimum Weight Triangulation.- A review of Machine Scheduling: Complexity, Algorithms and Approximability.- Algorithmic Aspects of Domination in Graphs.- The Quadratic Assignment Problem.- A Cognitive Algorithm for solving the Equal Circles Packing Problem.- Optimal Rectangular Partition.- Weighted Dominating Set in Unit Disk Graphs.- Part 3. Applications.- Applications of Set Covering, Set Packing and Set Partitioning Models: A Survey.- Combinatorial Optimization in Clustering.- Combinatorial Optimization and Coalition Games.- Optimization Problems in Optical Networks.- Optimization Applications in the Airline Industry.- Routing and Topology Embedding in Lightwave Networks.- Steiner Tree in Industry.- Connected Dominating Sets in Sensor Networks.- Network-based Model and Algorithms in Data Mining and Knowledge Discovery.- Steiner Tree in VISL Designs.- Steiner Tree in Coal Mining Industry.- Coverage Problems in sensor Networks.- Packing, Dominating and Wireless Networking.- Group Testing in Molecular Biology.- Index.
