An Approximate Maximum Common Subgraph Algorithm for Large Digital Circuits

Abstract

This paper presents an approximate Maximum Common Sub graph (MCS) algorithm, specifically for directed, cyclic graphs representing digital circuits. Because of the application domain, the graphs have nice properties: they are very sparse, have many different labels, and most vertices have only one predecessor. The algorithm iterates over all vertices once and uses heuristics to find the MCS. It is linear in computational complexity with respect to the size of the graph. Experiments show that very large common sub graphs were found in graphs of up to 200,000 vertices within a few minutes, when a quarter or less of the graphs differ. The variation in run-time and quality of the result is low.