By Hang T. Lau
As a result of its portability and platform-independence, Java is the best laptop programming language to exploit while engaged on graph algorithms and different mathematical programming difficulties. accumulating one of the most renowned graph algorithms and optimization techniques, 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 idea and combinatorial optimization. Self-contained and principally self reliant, each one subject starts off with an issue description and an overview of the answer strategy, through its parameter record specification, resource code, and a try out instance that illustrates the use of the code. The booklet starts with a bankruptcy on random graph new release that examines bipartite, average, attached, Hamilton, and isomorphic graphs in addition to spanning, categorized, and unlabeled rooted bushes. It then discusses connectivity approaches, through 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 concerning planarity and graph isomorphism. next chapters care for graph coloring, graph matching, community circulate, 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 extra information of the algorithms and comprise the definitions of many graph conception phrases utilized in the publication.
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Extra resources for A Java Library of Graph Algorithms and Optimization
Procedure parameters: void randomMaximumFlowNetwork (n, m, seed, minweight,maxweight, nodei, nodej, weight) n: int; entry: number of nodes of the network. Nodes of the graph are labeled from 1 to n. Node 1 is the source and node n is the sink. m: int; entry: number of required edges of the directed graph. seed: long; entry: seed for initializing the random number generator. minweight: int; entry: minimum weight of the edges. maxweight: int; entry: maximum weight of the edges. nodei, nodej: int[m+1]; exit: nodei returns the actual number of edges generated.
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. 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].
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.