By Hang T. Lau

Due to its portability and platform-independence, Java is the suitable desktop programming language to exploit whilst engaged on graph algorithms and different mathematical programming difficulties. gathering probably 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 conception and combinatorial optimization. Self-contained and principally self sufficient, 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 off with a bankruptcy on random graph iteration that examines bipartite, standard, hooked up, Hamilton, and isomorphic graphs in addition to spanning, classified, and unlabeled rooted timber. It then discusses connectivity systems, 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 strategies regarding planarity and graph isomorphism. next chapters take care of graph coloring, graph matching, community circulate, and packing and masking, together with the task, bottleneck task, quadratic task, a number of knapsack, set protecting, and set partitioning difficulties. the ultimate chapters discover linear, integer, and quadratic programming. The appendices offer 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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The method generates a random graph first, then a random permutation of n objects (perm[1], perm[2], …, perm[n]). The second isomorphic graph is obtained by renaming the vertices of the first random graph by the random permutation. The node i of the first random graph corresponds to the node perm[i] in the second graph. Procedure parameters: int randomIsomorphicGraphs (n, m, seed, simple, directed, firsti, firstj, secondi, secondj, map) randomIsomorphicGraph: int; exit: the method returns the following error code: 0: solution found with normal execution 1: 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.

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. 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.

The node i of the first random graph corresponds to the node perm[i] in the second graph. Procedure parameters: int randomIsomorphicGraphs (n, m, seed, simple, directed, firsti, firstj, secondi, secondj, map) randomIsomorphicGraph: int; exit: the method returns the following error code: 0: solution found with normal execution 1: 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. n: int; entry: number of nodes of each graph. Nodes of each graph are labeled from 1 to n.