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Multiple Canadians on the road: minimizing the distance competitive ratio

Author

Listed:
  • Pierre Bergé

    (Université Paris-Sud, Université Paris-Saclay)

  • Jean Desmarchelier

    (Université Paris-Saclay)

  • Wen Guo

    (Université Paris-Saclay)

  • Aurélie Lefebvre

    (Université Paris-Saclay)

  • Arpad Rimmel

    (Université Paris-Saclay)

  • Joanna Tomasik

    (Université Paris-Saclay)

Abstract

The online k-Canadian Traveller Problem ( $$k$$ k -CTP), known to be PSPACE-complete, asks for the best strategy a traveller has to follow in order to traverse with minimum distance a graph from s to t where at most k edges are blocked. A blocked edge is revealed when the traveller visits one of its endpoints. It is proven that for any deterministic strategy, the competitive ratio is larger than $$2k+1$$ 2 k + 1 . Indeed, the distance traversed by the traveller is potentially greater than $$2k+1$$ 2 k + 1 times the optimal journey. For randomized strategies, this ratio becomes $$k+1$$ k + 1 . We complement the work of Zhang et al. on $$k$$ k -CTP with multiple travellers by evaluating the distance competitive ratio of deterministic and randomized strategies for complete and partial communication. We compare these ratios with two other communication levels: when travellers do not communicate at all and when they communicate only before beginning to move. Eventually, we provide a wide picture of the distance competitiveness reachable for the $$k$$ k -CTP in function of the number of travellers and communication levels.

Suggested Citation

  • Pierre Bergé & Jean Desmarchelier & Wen Guo & Aurélie Lefebvre & Arpad Rimmel & Joanna Tomasik, 2019. "Multiple Canadians on the road: minimizing the distance competitive ratio," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1086-1100, November.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:4:d:10.1007_s10878-019-00438-6
    DOI: 10.1007/s10878-019-00438-6
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    References listed on IDEAS

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    1. Marco Bender & Stephan Westphal, 2015. "An optimal randomized online algorithm for the $$k$$ k -Canadian Traveller Problem on node-disjoint paths," Journal of Combinatorial Optimization, Springer, vol. 30(1), pages 87-96, July.
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