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On the Competitiveness of Memoryless Strategies for the k-Canadian Traveller Problem

  • Pierre Bergé
  • Julien Hemery
  • Arpad Rimmel
  • Joanna Tomasik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)

Abstract

The k-Canadian Traveller Problem (\(k\)-CTP), proven PSPACE-complete by Papadimitriou and Yannakakis, is a generalization of the Shortest Path Problem which admits blocked edges. Its objective is to determine the strategy that makes the traveller traverse graph G between two given nodes s and t with the minimal distance, knowing that at most k edges are blocked. The traveller discovers that an edge is blocked when arriving at one of its endpoints.

We study the competitiveness of randomized memoryless strategies to solve the \(k\)-CTP. Memoryless strategies are attractive in practice as a decision made by the strategy for a traveller in node v of G does not depend on his anterior moves. We establish that the competitive ratio of any randomized memoryless strategy cannot be better than \(2k + O\left( 1\right) \). This means that randomized memoryless strategies are asymptotically as competitive as deterministic strategies which achieve a ratio \(2k+1\) at best.

Keywords

Online algorithms Competitive analysis Canadian traveller problem 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Pierre Bergé
    • 1
  • Julien Hemery
    • 2
  • Arpad Rimmel
    • 2
  • Joanna Tomasik
    • 2
  1. 1.LRI, Université Paris-Sud, Université Paris-SaclayOrsayFrance
  2. 2.LRI, CentraleSupélec, Université Paris-SaclayOrsayFrance

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