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Heuristics with Constant Error Guarantees for the Design of Tree Networks

Author

Listed:
  • Kemal Altinkemer

    (Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana 47907)

  • Bezalel Gavish

    (Department of Administrative Sciences, Naval Postgraduate School, Monterey, California 93943)

Abstract

A tree network is a collection of trees rooted at a common central node. Several types of network design problems can be viewed as requiring the formation of a spanning tree network of minimum length, subject to a bound on the sum of "weights" on the nodes of any component tree. Such problems are NP-complete, and experience has shown that only small examples can be solved to optimality. This paper describes an efficient heuristic algorithm based on partitioning of a traveling salesman tour. When all the nodes have a unit weight and the bound is K, the heuristic finds a solution whose cost is at most 3 - 2/K times the minimum; in the general case the error bound is 4.

Suggested Citation

  • Kemal Altinkemer & Bezalel Gavish, 1988. "Heuristics with Constant Error Guarantees for the Design of Tree Networks," Management Science, INFORMS, vol. 34(3), pages 331-341, March.
    • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:3:p:331-341
    DOI: 10.1287/mnsc.34.3.331
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    Citations

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    Cited by:

    1. Kawatra, R. & Bricker, D., 2000. "A multiperiod planning model for the capacitated minimal spanning tree problem," European Journal of Operational Research, Elsevier, vol. 121(2), pages 412-419, March.
    2. Rakesh Kawatra, 2022. "Design of capacitated degree constrained min-sum arborescence," OPSEARCH, Springer;Operational Research Society of India, vol. 59(3), pages 1038-1054, September.
    3. Jianping Li & Wencheng Wang & Junran Lichen & Suding Liu & Pengxiang Pan, 2022. "Approximation algorithms for solving the line-capacitated minimum Steiner tree problem," Journal of Global Optimization, Springer, vol. 84(3), pages 687-714, November.
    4. Li, Xiaopeng & Medal, Hugh & Qu, Xiaobo, 2019. "Connected infrastructure location design under additive service utilities," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 99-124.
    5. Cruz, F. R. B. & Smith, J. MacGregor & Mateus, G. R., 1999. "Algorithms for a multi-level network optimization problem," European Journal of Operational Research, Elsevier, vol. 118(1), pages 164-180, October.
    6. Gupta, Rakesh & Pirkul, Hasan, 2000. "Hybrid fiber co-axial CATV network design with variable capacity optical network units," European Journal of Operational Research, Elsevier, vol. 123(1), pages 73-85, May.
    7. Raymond A. Patterson & Erik Rolland, 2002. "Hybrid Fiber Coaxial Network Design," Operations Research, INFORMS, vol. 50(3), pages 538-551, June.

    More about this item

    Keywords

    networks/graphs: design heuristics;

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