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Algorithms for the optimum communication spanning tree problem

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  • Prabha Sharma

Abstract

Optimum Communication Spanning Tree Problem is a special case of the Network Design Problem. In this problem given a graph, a set of requirements r ij and a set of distances d ij for all pair of nodes (i,j), the cost of communication for a pair of nodes (i,j), with respect to a spanning tree T is defined as r ij times the length of the unique path in T, that connects nodes i and j. Total cost of communication for a spanning tree is the sum of costs for all pairs of nodes of G. The problem is to construct a spanning tree for which the total cost of communication is the smallest among all the spanning trees of G. The problem is known to be NP-hard. Hu (1974) solved two special cases of the problem in polynomial time. In this paper, using Hu’s result the first algorithm begins with a cut-tree by keeping all d ij equal to the smallest d ij . For arcs (i,j) which are part of this cut-tree the corresponding d ij value is increased to obtain a near optimal communication spanning tree in pseudo-polynomial time. In case the distances d ij satisfy a generalised triangle inequality the second algorithm in the paper constructs a near optimum tree in polynomial time by parametrising on the r ij . Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Prabha Sharma, 2006. "Algorithms for the optimum communication spanning tree problem," Annals of Operations Research, Springer, vol. 143(1), pages 203-209, March.
    • Handle: RePEc:spr:annopr:v:143:y:2006:i:1:p:203-209:10.1007/s10479-006-7382-1
    DOI: 10.1007/s10479-006-7382-1
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    References listed on IDEAS

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    1. R. K. Ahuja & V. V. S. Murty, 1987. "Exact and Heuristic Algorithms for the Optimum Communication Spanning Tree Problem," Transportation Science, INFORMS, vol. 21(3), pages 163-170, August.
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    Cited by:

    1. Li, Gang & Balakrishnan, Anantaram, 2016. "Models and algorithms for network reduction," European Journal of Operational Research, Elsevier, vol. 248(3), pages 930-942.
    2. Zetina, Carlos Armando & Contreras, Ivan & Fernández, Elena & Luna-Mota, Carlos, 2019. "Solving the optimum communication spanning tree problem," European Journal of Operational Research, Elsevier, vol. 273(1), pages 108-117.
    3. Christian Tilk & Stefan Irnich, 2016. "Combined Column-and-Row-Generation for the Optimal Communication Spanning Tree Problem," Working Papers 1613, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    4. Yogesh Kumar Agarwal & Prahalad Venkateshan, 2019. "New Valid Inequalities for the Optimal Communication Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 268-284, April.

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