By Hang T. Lau

Due to its portability and platform-independence, Java is the best desktop programming language to exploit whilst engaged on graph algorithms and different mathematical programming difficulties. accumulating one of the most renowned graph algorithms and optimization tactics, A Java Library of Graph Algorithms and Optimization offers the resource code for a library of Java courses that may be used to resolve difficulties in graph thought and combinatorial optimization. Self-contained and principally autonomous, every one subject starts off with an issue description and an overview of the answer method, via its parameter record specification, resource code, and a try instance that illustrates the use of the code. The e-book starts with a bankruptcy on random graph iteration that examines bipartite, standard, hooked up, Hamilton, and isomorphic graphs in addition to spanning, categorised, 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 move, and packing and protecting, together with the task, bottleneck project, quadratic project, a number of knapsack, set overlaying, 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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**Extra resources for A Java Library of Graph Algorithms and Optimization**

**Sample text**

True : false; if (evenn) { // k is odd, n is even for (i=1; i<=halfn; i++) { edges++; nodei[edges] = i; nodej[edges] = i + halfn; } } else { // k is odd, n is odd p = (n + 1) / 2; q = (n - 1) / 2; for (i=2; i<=q; i++) { edges++; nodei[edges] = i; nodej[edges] = i + p; } edges++; nodei[edges] = 1; nodej[edges] = q + 1; edges++; nodei[edges] = 1; nodej[edges] = p + 1; } } © 2007 by Taylor & Francis Group, LLC Chapter 2: Connectivity 39 Example: Construct a 4-connected simple undirected graph on 8 nodes with the least number of edges.

Seed: seed for initializing the random number generator. directed = true if the graph is directed, false otherwise. weighted = true if the graph is weighted, false otherwise. minimum weight of the edges; if weighted = false then this value is ignored. maxweight: int; entry: maximum weight of the edges; if weighted = false then this value is ignored. 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.

NextDouble() * (maxweight + 1 - minweight)); } } return 0; } Example: Generate a random undirected connected simple graph of 8 nodes and 10 edges with edge weights in the range of [90, 99]. 9 Random Hamilton Graph The following procedure [JK91] generates a random simple Hamilton graph with some given number of nodes and 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]).