Including Geometry in Graph Representations: A Quadratic-Time Graph Isomorphism Algorithm and Its Application

In graph representations of objects, geometric information is typically lost. This has forced researchers to use graph matching techniques that are intended to handle general graphs. By encoding the lost geometric information into graph representations, however, we can apply more efficient algorithms for constrained graphs. In this paper we introduce an edge ordering property that is satisfied in many applications. Given this property, the graph isomorphism problem is solvable in quadratic time. We discuss three concrete applications that can be reduced to the graph isomorphism problem and can thus profit from the quadratic-time graph isomorphism algorithm. The improved performance is demonstrated by simulation experiments.