Tracking Paths in Planar Graphs

Abstract

We consider the NP-complete problem of tracking paths in a graph, first introduced by Banik et al. [Banik et al., 2017]. Given an undirected graph with a source s and a destination t, find the smallest subset of vertices whose intersection with any s-t path results in a unique sequence. In this paper, we show that this problem remains NP-complete when the graph is planar and we give a 4-approximation algorithm in this setting. We also show, via Courcelle\u27s theorem, that it can be solved in linear time for graphs of bounded-clique width, when its clique decomposition is given in advance