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) [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.

Ämnesord

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Sciences (hsv//eng)

Nyckelord

Canadian traveler problem

Complexity of navigation under uncertainty

Stochastic shortest path with recourse

NP-hard

Polynomial-time

PSPACE-complete

Stochastic shortest paths

Polynomial approximation

Stochastic systems

Graph theory

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