An exact algorithm for the maximum stable set problem
Computational Optimization and Applications
Ideal polytopes and face structures of some combinatorial optimization problems
Mathematical Programming: Series A and B
Anomalies in parallel branch-and-bound algorithms
Communications of the ACM
New methods to color the vertices of a graph
Communications of the ACM
Control Schemes in a Generalized Utility for Parallel Branch-and-Bound Algorithms
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
Joining Forces in Solving Large-Scale Quadratic Assignment Problems in Parallel
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
Building a parallel branch and bound library
Solving Combinatorial Optimization Problems in Parallel - Methods and Techniques
Optimizing neural networks on SIMD parallel computers
Parallel Computing
Simple ingredients leading to very efficient heuristics for the maximum clique problem
Journal of Heuristics
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Given an (undirected) graph G = (V, E), a clique of G is a subset of vertices in which every pair is connected by an edge. The problem of finding a clique of maximum size is a classical NP-hard problem, and many algorithms, both heuristic and exact, have been proposed. While the philosophy behind the heuristic algorithms varies greatly, almost all of the exact algorithms are designed in the branch-and-bound framework. As is well known, branch-and-bound is well suited to parallelization, and PUBB is a software utility which implements a generic version of it. In this paper, we show effectiveness of parallelization of branch-and-bound for the maximum clique problem. Especially, by using PUBB with good heuristics and branching techniques, we were able to solve five previously unsolved DIMACS benchmark problems to optimality.