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Exact and Heuristic Algorithms for the Optimum Communication Spanning Tree Problem

Author

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  • R. K. Ahuja

    (Indian Institute of Technology, Kanpur 208 016, India)

  • V. V. S. Murty

    (OMC Computers Ltd., Secunderabad, India)

Abstract

Network design problems have been widely investigated in the literature. In this paper, we study one such design problem, known as the Optimum Communication Spanning Tree (OCST) problem. We develop an exact algorithm based on the branch and bound approach and a heuristic algorithm to solve the problem. The branch and bound algorithm uses the lower planes recently developed by the authors. Reoptimization of subproblems is extensively used to reduce computation. The heuristic algorithm is a two-phase algorithm: tree-building algorithm and tree-improvement algorithm. These algorithms have been tested on randomly generated Euclidean and non-Euclidean problems and results of these investigations are described. The branch and bound algorithm is able to solve moderately large sized problems in reasonable time. The two-phase heuristic algorithm has produced excellent results by providing optimal solutions for all the problems tested. Further, it is capable of solving problems of size 100 nodes and 1,000 arcs in about 30 seconds on DEC 10.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:21:y:1987:i:3:p:163-170
    DOI: 10.1287/trsc.21.3.163
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    Cited by:

    1. Richard Church & John Current, 1993. "Maximal covering tree problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 129-142, February.
    2. Li, Gang & Balakrishnan, Anantaram, 2016. "Models and algorithms for network reduction," European Journal of Operational Research, Elsevier, vol. 248(3), pages 930-942.
    3. 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.
    4. 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.
    5. 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.
    6. Prabha Sharma, 2006. "Algorithms for the optimum communication spanning tree problem," Annals of Operations Research, Springer, vol. 143(1), pages 203-209, March.
    7. Ivan Contreras & Elena Fernández & Alfredo Marín, 2010. "Lagrangean bounds for the optimum communication spanning tree problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 140-157, July.
    8. Hui Chen & Ann Melissa Campbell & Barrett W. Thomas, 2008. "Network design for time‐constrained delivery," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(6), pages 493-515, September.

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