A Java Library of Graph Algorithms and Optimization - download pdf or read online

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 suitable laptop programming language to exploit while engaged on graph algorithms and different mathematical programming difficulties. gathering essentially the most well known graph algorithms and optimization strategies, 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 principally autonomous, each one subject starts off with an issue description and an summary of the answer method, through its parameter checklist specification, resource code, and a try instance that illustrates using the code. The publication starts with a bankruptcy on random graph new release that examines bipartite, typical, attached, Hamilton, and isomorphic graphs in addition to spanning, categorized, and unlabeled rooted timber. It then discusses connectivity strategies, by means 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 try out methods related to planarity and graph isomorphism. next chapters care for graph coloring, graph matching, community stream, and packing and overlaying, together with the project, bottleneck project, quadratic task, a number of knapsack, set masking, 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 concept phrases utilized in the booklet.

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Extra resources for A Java Library of Graph Algorithms and Optimization

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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.

Case 1: (k is odd, n is odd) Let k = 2t+1. The graph G(2t+1,n) is constructed by first drawing G(2t,n), and then joining: node 0 to node (n−1)/2, node 0 to node (n+1)/2, node i to node i+(n+1)/2, for 1 ≤ i < (n−1)/2. Procedure parameters: void maximumConnectivity (n, k, nodei, nodej) n: int; entry: k: int; entry: nodei, nodej: exit: the number of nodes of the undirected graph, labeled from 1 to n. the required graph is k-connected, k ≥ 2. int[ ⎡(n∗k)/2⎤ + 1]; nodei[p] and nodej[p] are the end nodes of the p-th edge in the k-connected graph, p=1,2,…, ⎡(n∗k)/2⎤.

1 Maximum Connectivity Given two positive integers n and k, the following procedure [H62] constructs a k-connected simple undirected graph G(k,n) on n nodes with the least number of edges. It is known that G(k,n) has exactly ⎡(n∗k)/2⎤ edges, where ⎡x⎤ is the smallest integer greater than or equal to x. Note that G(1,n) is a spanning tree. It is assumed that k ≥ 2. Let the nodes of the graph be integers 0,1,2,…,n−1. Case 1: (k is even) Let k = 2t. The graph G(2t,n) is constructed as follows. Draw an n-gon, that is, add the edges (0,1), (1,2), (2,3), …, (n−2,n−1), (n−1,0).

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


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