Complexity of Canadian Traveler Problem Variants

Dror Fried; Solomon Eyal Shimony; Amit Benbassat; Cenny Wenner

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arXiv · 1207.4710

Complexity of Canadian Traveler Problem Variants

Dror Fried·Solomon Eyal Shimony·Amit Benbassat·Cenny Wenner

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Abstract

The Canadian traveler problem (CTP) is the problem of traversing a given graph, where some of the edges may be blocked - a state which is revealed only upon reaching an incident vertex. Originally stated by Papadimitriou and Yannakakis (1991), the adversarial version of CTP was shown to be PSPACE-complete, with the stochastic version shown to be #P-hard. We show that stochastic CTP is also PSPACE-complete: initially proving PSPACE-hardness for the dependent version of stochastic CTP,and proceeding with gadgets that allow us to extend the proof to the independent case. Since for disjoint-path graphs, CTP can be solved in polynomial time, we examine the complexity of the more general remote-sensing CTP, and show that it is NP-hard even for disjoint-path graphs.

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Dror Fried, Solomon Eyal Shimony, Amit Benbassat, Cenny Wenner. 2012-07-19. Complexity of Canadian Traveler Problem Variants. https://arxiv.org/abs/1207.4710

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