For a given graph G, minimum stretch spanning tree problem (MSSTP) seeks for a spanning tree of G such that the distance between the farthest pair of adjacent vertices of G in tree is minimized. It is an NP-hard problem with applications in communication networks. In this paper, a general variable neighborhood search (GVNS) algorithm is developed for MSSTP in which initial solution is generated using four well-known heuristics and a problem-specific construction heuristic. Six neighborhood strategies are designed to explore the search space. The experiments are conducted on various classes of graphs for which optimal results are known. Computational results show that the proposed algorithm is better than the artificial bee colony (ABC) algorithm which is adapted by us for MSSTP.
Given an undirected connected graph G, the profile minimization problem (PMP) is to place the vertices of G in a linear layout (labeling) in such a way that the sum of profiles of the vertices in G is minimized, where the profile of a vertex is the difference of its labeling with the labeling of its left most neighbor in the layout. It is an NP-complete problem and has applications in various areas such as numerical analysis, fingerprinting, and information retrieval. In this paper, we design a tabuembedded simulated annealing algorithm for profile reduction (TSAPR) for PMP which uses a well-known spectral sequencing method to generate an initial solution. An efficient technique is employed to compute the profile of a neighbor of a solution. The experiments are conducted on different classes of graphs such as T 4 -trees, tensor product of graphs, complete bipartite graphs, triangulated triangle graphs, and a subset of Harwell-Boeing graphs. The computational results demonstrate an improvement in the existing results by TSAPR in most of the cases.
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