Space-Efficient Algorithms for Reachability in Geometric Graphs

The problem of graph Reachability is to decide whether there is a path from one vertex to another in a given graph. In this paper, we study the Reachability problem on three distinct graph families -- intersection graphs of Jordan regions, unit contact disk graphs (penny graphs), and chordal graphs. For each of these graph families, we present space-efficient algorithms for the Reachability problem. In order to obtain these results, we use the vertex separator of these graphs effectively, and design space-efficient algorithms to find such separators. The constructions of the separators presented here can be of independent interest.