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Faster Swap Edge Computation in Minimum Diameter Spanning Trees

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Abstract

In network communication systems, frequently messages are routed along a minimum diameter spanning tree (MDST) of the network, to minimize the maximum travel time of messages. When a transient failure disables an edge of the MDST, the network is disconnected, and a temporary replacement edge must be chosen, which should ideally minimize the diameter of the new spanning tree. Such a replacement edge is called a best swap. Preparing for the failure of any edge of the MDST, the all-best-swaps (ABS) problem asks for finding the best swap for every edge of the MDST. Given a 2-edge-connected weighted graph G=(V,E), where |V|=n and |E|=m, we solve the ABS problem in O(mlog n) time and O(m) space, thus considerably improving upon the decade-old previously best solution, which requires \(O(n\sqrt{m})\) time and O(m) space, for m=o(n 2/log 2 n).

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Authors and Affiliations

  1. IBM Research Zurich, Säumerstrasse 4, 8803, Rüschlikon, Switzerland

    Beat Gfeller

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  1. Beat Gfeller
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Correspondence to Beat Gfeller.

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A preliminary version of this paper appeared in the Proceedings of the 16th Annual European Symposium on Algorithms (ESA), 2008.

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Gfeller, B. Faster Swap Edge Computation in Minimum Diameter Spanning Trees. Algorithmica 62, 169–191 (2012). https://doi.org/10.1007/s00453-010-9448-3

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  • DOI: https://doi.org/10.1007/s00453-010-9448-3

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