Complexity of Canadian traveler problem variants

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.