2014/01/23 by Ciaran McCreesh, McCreesh, Ciaran, Patrick Prosser +1
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Constraint Satisfaction and Optimization #Distributed #FOS: Computer and information sciences #Optimization and Search Problems #Parallel #and Cluster Computing (cs.DC) #cs.DC
paper · pdf · doi:10.48550/arxiv.1401.5921
Substantial revision
openalex publication_date 2014/01/23 · arxiv created 2014/09/04 · arxiv updated 2014/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel explanation as to why they are successful. We show that load balance is sometimes a problem, but that the interaction of parallel search order and the most likely location of solutions within the search space is often the dominating consideration. We use this explanation to propose a new low-overhead, scalable work splitting mechanism. Our approach uses explicit early diversity to avoid strong commitment to the weakest heuristic advice, and late resplitting for balance. More generally, we argue that for branch and bound, parallel algorithm design should not be performed independently of the underlying sequential algorithm.