Browsing by Subject "Spanning tree"

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    New formulations for the hop-constrained minimum spanning tree problem via Sherali and Driscoll's tightened Miller-Tucker-Zemlin constraints
    (Elsevier, 2010) Akgün, İbrahim
    Given an undirected network with positive edge costs and a natural number p, the hop-constrained minimum spanning tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, the new models based on the Miller-Tucker-Zemlin (MTZ) subtour elimination constraints are developed and computational results together with comparisons against MTZ-based, flow-based, and hop-indexed formulations are reported. The first model is obtained by adapting the MTZ-based Asymmetric Traveling Salesman Problem formulation of Sherali and Driscoll [18] and the other two models are obtained by combining topology-enforcing and MTZ-related constraints offered by Akgün and Tansel (submitted for publication) [20] for HMST with the first model appropriately. Computational studies show that the best LP bounds of the MTZ-based models in the literature are improved by the proposed models. The best solution times of the MTZ-based models are not improved for optimally solved instances. However, the results for the harder, large-size instances imply that the proposed models are likely to produce better solution times. The proposed models do not dominate the flow-based and hop-indexed formulations with respect to LP bounds. However, good feasible solutions can be obtained in a reasonable amount of time for problems for which even the LP relaxations of the flow-based and hop-indexed formulations can be solved in about 2 days. © 2010 Elsevier Ltd. All rights reserved.
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    The robust spanning tree problem with interval data
    (Elsevier, 2001) Yaman, H.; Karaşan, O. E.; Pınar, M. Ç.
    Motivated by telecommunications applications we investigate the minimum spanning tree problem where edge costs are interval numbers. Since minimum spanning trees depend on the realization of the edge costs, we de5ne the robust spanning tree problem to hedge against the worst case contingency, and present a mixed integer programming formulation of the problem. We also de5ne some useful optimality concepts, and present characterizations for these entities leading to polynomial time recognition algorithms. These entities are then used to preprocess a given graph with interval data prior to the solution of the robust spanning tree problem. Computational results show that these preprocessing procedures are quite e9ective in reducing the time to compute a robust spanning tree.
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    A spanning tree approach to the absolute p-center problem
    (Elsevier, 1998) Bozkaya, B.; Tansel, B.
    We consider the absolute p-center problem on a general network and propose a spanning tree approach which is motivated by the fact that the problem is NP-hard on general networks but solvable in polynomial time on trees. We first prove that every connected network possesses a spanning tree whose p-center solution is also a solution for the network under consideration. Then we propose two classes of spanning trees that are shortest path trees rooted at certain points of the network. We give an experimental study, based on 1440 instances, to test how often these classes of trees include an optimizing tree. We report our computational results on the performance of both types of trees. © 1999 Elsevier Science Ltd. All rights reserved.