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Journal of Combinatorial Optimization

, Volume 30, Issue 1, pp 87–96 | Cite as

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

  • Marco Bender
  • Stephan Westphal
Article

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.

Keywords

Competitive analysis Online algorithm Canadian Traveller Problem 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute for Numerical and Applied MathematicsUniversity of GöttingenGöttingenGermany

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