Complexity of Canadian Traveler Problem Variants

TL;DR

This paper investigates the computational complexity of various versions of the Canadian Traveler Problem, establishing new hardness results and extending known complexity classifications for stochastic and remote-sensing variants.

Contribution

It proves that stochastic CTP is PSPACE-complete and shows NP-hardness of remote-sensing CTP on disjoint-path graphs, advancing understanding of the problem's complexity.

Findings

Stochastic CTP is PSPACE-complete.

Remote-sensing CTP is NP-hard on disjoint-path graphs.

Dependent stochastic CTP is PSPACE-hard.

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), 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.