A note on the k-Canadian Traveller Problem

Authors:
Stephan Westphal
Affiliations:
University of Kaiserslautern, Department of Mathematics, P.O. Box 3049, Paul-Ehrlich-Str. 14, 67653 Kaiserslautern, Germany
Venue:
Information Processing Letters
Year:
2008

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Abstract

We consider the online problem k-CTP, which is the problem to guide a vehicle from some site s to some site t on a road map given by a graph G=(V,E) in which up to k (unknown) edges are blocked by avalanches. An online algorithm learns from a blocked edge when reaching one of its endpoints. Thus, it might have to change its route to the target t up to k times. We show that no deterministic online algorithm can achieve a competitive ratio smaller than 2k+1 and give an easy algorithm which matches this lower bound. Furthermore, we show that randomization can not improve the competitive ratio substantially, by establishing a lower bound of k+1 for the competitivity of randomized online algorithms against an oblivious adversary.