TY - JOUR

T1 - Complexity of Canadian traveler problem variants

AU - Fried, Dror

AU - Shimony, Solomon Eyal

AU - Benbassat, Amit

AU - Wenner, Cenny

N1 - Funding Information:
This research is partially supported by the Israel Science Foundation grant 305/09, the Lynn and William Frankel Center for Computer Sciences, and by ERC Advanced Investigator Grant 226203. We thank the anonymous reviewers for insightful, and deep suggestions, that improved the paper significantly.

PY - 2013/5/27

Y1 - 2013/5/27

N2 - 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) [1], the adversarial version of the CTP was shown to be PSPACE-complete, with the stochastic version shown to be in PSPACE and #P-hard. We show that the stochastic CTP is also PSPACE-complete: initially proving PSPACE-hardness for the dependent version of the stochastic CTP, and proceeding with gadgets that allow us to extend the proof to the independent case. Since for disjoint-path graphs, the 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.

AB - 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) [1], the adversarial version of the CTP was shown to be PSPACE-complete, with the stochastic version shown to be in PSPACE and #P-hard. We show that the stochastic CTP is also PSPACE-complete: initially proving PSPACE-hardness for the dependent version of the stochastic CTP, and proceeding with gadgets that allow us to extend the proof to the independent case. Since for disjoint-path graphs, the 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.

KW - Canadian traveler problem

KW - Complexity of navigation under uncertainty

KW - Stochastic shortest path with recourse

UR - http://www.scopus.com/inward/record.url?scp=84877577190&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2013.03.016

DO - 10.1016/j.tcs.2013.03.016

M3 - Article

AN - SCOPUS:84877577190

VL - 487

SP - 1

EP - 16

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -