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. 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 \( O\left( m\log n \right) \) 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 \(m=o\left(n^2/ \log^2 n\right)\).
We gratefully acknowledge the support of the Swiss SBF under contract no. C05.0047 within COST-295 (DYNAMO) of the European Union.
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Gfeller, B. (2008). Faster Swap Edge Computation in Minimum Diameter Spanning Trees. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_38
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DOI: https://doi.org/10.1007/978-3-540-87744-8_38
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