By Hang T. Lau

ISBN-10: 1584887184

ISBN-13: 9781584887188

ISBN-10: 1584887192

ISBN-13: 9781584887195

Due to its portability and platform-independence, Java is the right computing device programming language to take advantage of while engaged on graph algorithms and different mathematical programming difficulties. accumulating essentially the most well known graph algorithms and optimization systems, 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 concept and combinatorial optimization. Self-contained and mostly self sustaining, every one subject starts off with an issue description and an overview of the answer process, via its parameter checklist specification, resource code, and a attempt instance that illustrates the use of the code. The ebook starts with a bankruptcy on random graph iteration that examines bipartite, common, hooked up, Hamilton, and isomorphic graphs in addition to spanning, categorised, and unlabeled rooted bushes. It then discusses connectivity strategies, by way of a paths and cycles bankruptcy that comprises the chinese language postman and touring salesman difficulties, Euler and Hamilton cycles, and shortest paths. the writer proceeds to explain attempt methods regarding planarity and graph isomorphism. next chapters take care of graph coloring, graph matching, community stream, and packing and protecting, together with the task, bottleneck project, quadratic task, 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 extra info of the algorithms and comprise the definitions of many graph idea phrases utilized in the publication.

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**Example text**

A cut node of a component is a node whose removal will disconnect the component. The following procedure [P71] finds the number of components and all the cut nodes for a given simple undirected graph of n nodes in time O(n2). The set of nodes V of the input graph G are assumed to be numbered from 1 to n. A tree T rooted at a node r will be grown to span G. Let p(i) denote the unique predecessor of each node i in the tree, d(i) be the distance from node i to the root of T, b(i) be the label assigned to the edge (i,p(i)), and h(j) be a Boolean variable for marking edge j.

True : false; for (i=1; i<=nminus1; i++) { p = i + 1; for (j=p; j<=n; j++) { join = false; q = j - i; for (r=2; r<=halfk; r++) if (((r - ((r/n)*n)) == q) || (q + r == n)) join = true; if (join) { edges++; nodei[edges] = i; nodej[edges] = j; } } } // if k is even then finish if (evenk) return; evenn = (n == 2 * halfn) ? 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.

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.

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

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