Improved Deterministic Strategy for the Canadian Traveller Problem Exploiting Small Max-(st)-Cuts

  • Pierre BergéEmail author
  • Lou Salaün
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11926)


The k-Canadian Traveller Problem consists in finding the optimal way from a source s to a target t on an undirected weighted graph G, knowing that at most k edges are blocked. The traveller, guided by a strategy, sees an edge is blocked when he visits one of its endpoints. A major result established by Westphal is that the competitive ratio of any deterministic strategy for this problem is at least \(2k+1\). reposition and comparison strategies achieve this bound.

We refine this analysis by focusing on graphs with a maximum (st)-cut size \(\mu _{\text {max}}\) less than k. A strategy called detour is proposed and its competitive ratio is \(2\mu _{\text {max}}+ \sqrt{2}(k-\mu _{\text {max}}) + 1\) when \(\mu _{\text {max}}< k\) which is strictly less than \(2k+1\). Moreover, when \(\mu _{\text {max}}\ge k\), the competitive ratio of detour is \(2k+1\) and is optimal. Therefore, detour improves the competitiveness of the deterministic strategies known up to now.


Canadian traveller problem Competitive analysis Online algorithms 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.LRI, Université Paris-Sud, Université Paris-SaclayOrsayFrance
  2. 2.Bell Labs, Nokia Paris-SaclayNozayFrance
  3. 3.LTCI, Telecom ParisTech, Université Paris-SaclayParisFrance

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