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An optimal randomized online algorithm for the \(k\)-Canadian Traveller Problem on node-disjoint paths

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Abstract

We consider the \(k\)-Canadian Traveller Problem, which asks for a shortest path between two nodes \(s\) and \(t\) in an undirected graph, where up to \(k\) edges may be blocked. An online algorithm learns about a blocked edge when reaching one of its endpoints. Recently, it has been shown that no randomized online algorithm can be better than \((k+1)\)-competitive, even if all \(s\)-\(t\)-paths are node-disjoint. We show that the bound is tight by constructing a randomized online algorithm for this case that achieves the ratio against an oblivious adversary and is therefore best possible.

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Authors and Affiliations

  1. Institute for Numerical and Applied Mathematics, University of Göttingen, Göttingen, Germany

    Marco Bender & Stephan Westphal

Authors
  1. Marco Bender
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  2. Stephan Westphal
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Correspondence to Marco Bender.

Additional information

Marco Bender was partially supported by DFG RTG 1703 “Resource Efficiency in Interorganizational Networks”.

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Bender, M., Westphal, S. An optimal randomized online algorithm for the \(k\)-Canadian Traveller Problem on node-disjoint paths. J Comb Optim 30, 87–96 (2015). https://doi.org/10.1007/s10878-013-9634-8

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  • DOI: https://doi.org/10.1007/s10878-013-9634-8

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