A Java Library of Graph Algorithms and Optimization

A Java Library of Graph Algorithms and Optimization

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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.
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Product details

  • Electronic book text | 386 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 1584887192
  • 9781584887195

Table of contents

INTRODUCTIONRANDOM GRAPH GENERATIONRandom Permutation of n Objects Random GraphRandom Bipartite GraphRandom Regular Graph Random Spanning TreeRandom Labeled Tree Random Unlabeled Rooted TreeRandom Connected GraphRandom Hamilton GraphRandom Maximum Flow Network Random Isomorphic GraphsRandom Isomorphic Regular Graphs CONNECTIVITYMaximum Connectivity Depth-First Search Breadth-First SearchConnected Graph TestingConnected Components Cut NodesStrongly Connected Components Minimal Equivalent Graph Edge ConnectivityMinimum Spanning TreeAll CliquesPATHS AND CYCLES Fundamental Set of Cycles Shortest Cycle LengthOne-Pair Shortest Path All Shortest Path Length Shortest Path TreeAll Pairs Shortest Paths k Shortest Pathsk Shortest Paths without Repeated Nodes Euler Circuit Hamilton Cycle Chinese Postman TourTraveling Salesman Problem PLANARITY TESTINGGRAPH ISOMORPHISM TESTINGCOLORING Node ColoringChromatic PolynomialGRAPH MATCHING Maximum Cardinality MatchingMinimum Sum Perfect MatchingNETWORK FLOW Maximum Network FlowMinimum Cost Network FlowPACKING AND COVERINGAssignment Problem Bottleneck Assignment Problem Quadratic Assignment ProblemMultiple Knapsack Problem Set Covering Problem Set Partitioning ProblemLINEAR PROGRAMMINGRevised Simplex Method Dual Simplex MethodINTEGER PROGRAMMINGZero-One Integer ProgrammingAll Integer Programming Mixed Integer ProgrammingQUADRATIC PROGRAMMINGAPPENDIX A: REFERENCESAPPENDIX B: GRAPH-THEORETIC TERMS INDEX OF PROCEDURES
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