Faster Enumeration of All Maximal Cliques in Unit Disk Graphs Using Geometric Structure

This paper considers the problem of enumerating all maximal cliques in unit disk graphs, which is a plausible setting for applications of finding similar data groups. Our primary interest is to develop a faster algorithm using the geometric structure about the metric space where the input unit disk graph is embedded. Assuming that the distance between any two vertices is available, we propose a new algorithm based on two well-known algorithms called Bron-Kerbosch and Tomita-Tanaka-Takahashi. The key idea of our algorithm is to find a good pivot quickly using geometric proximity. We validate the practical impact of our algorithm via experimental evaluations.