2018-04-17
Approximation and complexity of multi-target graph search and the Canadian traveler problem
Publication
Publication
Theoretical Computer Science , Volume 732 p. 14- 25
In the Canadian traveler problem, we are given an edge weighted graph with two specified vertices s and t and a probability distribution over the edges that tells which edges are present. The goal is to minimize the expected length of a walk from s to t. However, we only get to know whether an edge is active the moment we visit one of its incident vertices. Under the assumption that the edges are active independently, we show NP-hardness on series-parallel graphs and give results on the adaptivity gap. We further show that this problem is NP-hard on disjoint-path graphs and cactus graphs when the distribution is given by a list of scenarios. We also consider a special case called the multi-target graph search problem. In this problem, we are given a probability distribution over subsets of vertices. The distribution specifies which set of vertices has targets. The goal is to minimize the expected length of the walk until finding a target. For the independent decision model, we show that the problem is NP-hard on trees and give a (3.59+ϵ)-approximation for trees and a (14.4+ϵ)-approximation for general metrics. For the scenario model, we show NP-hardness on star graphs.
Additional Metadata | |
---|---|
, , , , | |
doi.org/10.1016/j.tcs.2018.04.022 | |
Theoretical Computer Science | |
Organisation | Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
van Ee, M., & Sitters, R. (2018). Approximation and complexity of multi-target graph search and the Canadian traveler problem. Theoretical Computer Science, 732, 14–25. doi:10.1016/j.tcs.2018.04.022 |