Using symbolic techniques to find the maximum clique in very large sparse graphs

Several problems arising in CAD for VLSI, especially in logic and high level synthesis, are modeled as graph-theoretical problems. In particular minimization problems often require the knowledge of the cliques in a graph. This paper presents a new approach for finding the maximum clique in realistic graphs. The algorithm is built around a classical branch-and-bound, but exploits the efficiency of Binary Decision Diagrams and Symbolic Techniques to avoid explicit enumeration of the search space. The approach is proven to be more efficient than classical algorithms, which suffer from the enumeration problem, as well as purely symbolic implementations, which suffer from the explosion in the size of BDDs. As a result, we are able to compute the maximum clique without introducing approximations for graphs with billions of vertices and transitions