## 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) [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.

Original language | English |
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Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Theoretical Computer Science |

Volume | 487 |

DOIs | |

State | Published - 27 May 2013 |

Externally published | Yes |

### Bibliographical note

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.

## Keywords

- Canadian traveler problem
- Complexity of navigation under uncertainty
- Stochastic shortest path with recourse