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The Performance of greedy algorithms for the on-line steiner tree and related problems

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Abstract

We study the on-line Steiner tree problem on a general metric space. We show that the greedy on-line algorithm isO(log((d/z)s))-competitive, wheres is the number of regular nodes,d is the maximum metric distance between any two revealed nodes, andz is the optimal off-line cost. Our results refine the previous known bound [9] and show that AlgorithmSB of Bartalet al. [3] for the on-line file allocation problem isO(log logN)-competitive on anN-node hypercube or butterfly network. A lower bound of Ω(log((d/z)s)) is shown to hold.

We further consider the on-line generalized Steiner problem on a general metric space. We show that a class of lazy and greedy deterministic on-line algorithms areO(√k· logk)-competitive and no on-line algorithm is better than Ω(logk)-competitive, wherek is the number of distinct nodes that appear in the request sequence.

For the on-line Steiner problem on a directed graph, it is shown that no deterministic on-line algorithm is better thans-competitive and the greedy on-line algorithm iss-competitive.

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Authors and Affiliations

  1. Department of Computer Science, Yale University, 06520-2158, New Haven, CT, USA

    J. Westbrook

  2. Department of Operations Research, Yale University, 06520-0162, New Haven, CT, USA

    D. C. K. Yan

Authors
  1. J. Westbrook
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  2. D. C. K. Yan
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Additional information

A preliminary version of this paper has appeared in theProceedings of the Workshop on Algorithms and Data Structures, 1993, Montréal. The first author's research was partially supported by NSF Grant CCR-9009753, whilst that of the second author was partially supported by NSF Grant DDM-8909660 and a University Fellowship from the Graduate School, Yale University.

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Westbrook, J., Yan, D.C.K. The Performance of greedy algorithms for the on-line steiner tree and related problems. Math. Systems Theory 28, 451–468 (1995). https://doi.org/10.1007/BF01185867

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  • DOI: https://doi.org/10.1007/BF01185867

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