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
SN - 0304-3975
VL - 487
SP - 1
EP - 16
JO - Theoretical Computer Science
JF - Theoretical Computer Science
ER -