Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Finding a maximum clique in an arbitrary graph
SIAM Journal on Computing
TABARIS: an exact algorithm based on Tabu Search for finding a maximum independent set in a graph
Computers and Operations Research
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Efficient implementation of a BDD package
DAC '90 Proceedings of the 27th ACM/IEEE Design Automation Conference
Zero-suppressed BDDs for set manipulation in combinatorial problems
DAC '93 Proceedings of the 30th international Design Automation Conference
Algorithm 457: finding all cliques of an undirected graph
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Hypergraph Coloring and Reconfigured RAM Testing
IEEE Transactions on Computers
Hybrid symbolic-explicit techniques for the graph coloring problem
EDTC '97 Proceedings of the 1997 European conference on Design and Test
SPIDA: Abstracting and generalizing layout design cases
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
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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.