A Java Library of Graph Algorithms and Optimization (Discrete Mathematics and Its Applications)

A Java Library of Graph Algorithms and Optimization (Discrete Mathematics and Its Applications)

By: Hang T. Lau (author)Hardback

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Because of its portability and platform-independence, Java is the ideal computer programming language to use when working on graph algorithms and other mathematical programming problems. Collecting some of the most popular graph algorithms and optimization procedures, A Java Library of Graph Algorithms and Optimization provides the source code for a library of Java programs that can be used to solve problems in graph theory and combinatorial optimization. Self-contained and largely independent, each topic starts with a problem description and an outline of the solution procedure, followed by its parameter list specification, source code, and a test example that illustrates the usage of the code. The book begins with a chapter on random graph generation that examines bipartite, regular, connected, Hamilton, and isomorphic graphs as well as spanning, labeled, and unlabeled rooted trees. It then discusses connectivity procedures, followed by a paths and cycles chapter that contains the Chinese postman and traveling salesman problems, Euler and Hamilton cycles, and shortest paths. The author proceeds to describe two test procedures involving planarity and graph isomorphism. Subsequent chapters deal with graph coloring, graph matching, network flow, and packing and covering, including the assignment, bottleneck assignment, quadratic assignment, multiple knapsack, set covering, and set partitioning problems. The final chapters explore linear, integer, and quadratic programming. The appendices provide references that offer further details of the algorithms and include the definitions of many graph theory terms used in the book.


INTRODUCTION RANDOM GRAPH GENERATION Random Permutation of n Objects Random Graph Random Bipartite Graph Random Regular Graph Random Spanning Tree Random Labeled Tree Random Unlabeled Rooted Tree Random Connected Graph Random Hamilton Graph Random Maximum Flow Network Random Isomorphic Graphs Random Isomorphic Regular Graphs CONNECTIVITY Maximum Connectivity Depth-First Search Breadth-First Search Connected Graph Testing Connected Components Cut Nodes Strongly Connected Components Minimal Equivalent Graph Edge Connectivity Minimum Spanning Tree All Cliques PATHS AND CYCLES Fundamental Set of Cycles Shortest Cycle Length One-Pair Shortest Path All Shortest Path Length Shortest Path Tree All Pairs Shortest Paths k Shortest Paths k Shortest Paths without Repeated Nodes Euler Circuit Hamilton Cycle Chinese Postman Tour Traveling Salesman Problem PLANARITY TESTING GRAPH ISOMORPHISM TESTING COLORING Node Coloring Chromatic Polynomial GRAPH MATCHING Maximum Cardinality Matching Minimum Sum Perfect Matching NETWORK FLOW Maximum Network Flow Minimum Cost Network Flow PACKING AND COVERING Assignment Problem Bottleneck Assignment Problem Quadratic Assignment Problem Multiple Knapsack Problem Set Covering Problem Set Partitioning Problem LINEAR PROGRAMMING Revised Simplex Method Dual Simplex Method INTEGER PROGRAMMING Zero-One Integer Programming All Integer Programming Mixed Integer Programming QUADRATIC PROGRAMMING APPENDIX A: REFERENCES APPENDIX B: GRAPH-THEORETIC TERMS INDEX OF PROCEDURES

Product Details

  • ISBN13: 9781584887188
  • Format: Hardback
  • Number Of Pages: 386
  • ID: 9781584887188
  • weight: 870
  • ISBN10: 1584887184

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