By Hang T. Lau

ISBN-10: 1584887184

ISBN-13: 9781584887188

ISBN-10: 1584887192

ISBN-13: 9781584887195

As a result of its portability and platform-independence, Java is the fitting computing device programming language to exploit whilst engaged on graph algorithms and different mathematical programming difficulties. accumulating the most renowned graph algorithms and optimization methods, A Java Library of Graph Algorithms and Optimization presents the resource code for a library of Java courses that may be used to resolve difficulties in graph conception and combinatorial optimization. Self-contained and principally self sufficient, each one subject begins with an issue description and an summary of the answer process, through its parameter checklist specification, resource code, and a attempt instance that illustrates using the code. The publication starts off with a bankruptcy on random graph iteration that examines bipartite, normal, hooked up, Hamilton, and isomorphic graphs in addition to spanning, categorized, and unlabeled rooted bushes. It then discusses connectivity systems, by means of a paths and cycles bankruptcy that includes the chinese language postman and touring salesman difficulties, Euler and Hamilton cycles, and shortest paths. the writer proceeds to explain try out approaches concerning planarity and graph isomorphism. next chapters take care of graph coloring, graph matching, community stream, and packing and masking, together with the task, bottleneck project, quadratic task, a number of knapsack, set protecting, and set partitioning difficulties. the ultimate chapters discover linear, integer, and quadratic programming. The appendices supply references that supply additional information of the algorithms and contain the definitions of many graph thought phrases utilized in the ebook.

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Choose any node from the next component of the graph and repeat the same procedure. The algorithm terminates when all nodes are visited. The running time is O(max(n,m)), where n is the number of nodes and m is the number of edges of the graph. © 2007 by Taylor & Francis Group, LLC A Java Library of Graph Algorithms and Optimization 44 Procedure parameters: void breadthFirstSearch (n, m, nodei, nodej, parent, sequence) n: int; entry: number of nodes of the undirected graph, nodes of the graph are labeled from 1 to n.

Nodei, nodej: int[m+1]; exit: the i-th edge is from node nodei[i] to node nodej[i], for i = 1,2,…,m. The Hamilton cycle is given by the first n elements of these two arrays. weight: int[m+1]; exit: weight[i] is the weight of the i-th edge, for i = 1,2,…,m; if weighted = false then this array is ignored. nextDouble() * (maxweight + 1 - minweight)); } } return 0; } Example: Generate a random simple Hamilton graph of 7 nodes and 10 edges with edge weights in the range of [90, 99]. 10 Random Maximum Flow Network The following procedure [JK91] generates a random simple weighted directed graph of n nodes in which node 1 (the source) has no incoming edges and node n (the sink) has no outgoing edges.

The graph can be directed or undirected. The method generates a random permutation of n objects (perm[1], perm[2], …, perm[n]). The graph is initialized with the Hamilton cycle (perm[1], perm[2]), (perm[2], perm[3]), …, (perm[n−1], perm[n]), (perm[n], perm[1]). Then random edges are added into the graph until the required number of edges is reached. Procedure parameters: int randomHamiltonGraph (n, m, seed, directed, weighted, minweight, maxweight, nodei, nodej, weight) randomHamiltonGraph: int; exit: the method returns the following error code: 0: solution found with normal execution 1: value of m is too small, should be at least n 2: value of m is too large, should be at most n∗(n−1)/2 for simple undirected graph, and n∗(n-1) for simple directed graph.

### A Java Library of Graph Algorithms and Optimization by Hang T. Lau

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