The shape of the search tree for the maximum clique problem, and the implications for parallel branch and bound

McCreesh, C. and Prosser, P. (2015) The shape of the search tree for the maximum clique problem, and the implications for parallel branch and bound. ACM Transactions on Parallel Computing, 2(1), 8. (doi:10.1145/2742359)

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Abstract

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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Prosser, Dr Patrick and Mccreesh, Dr Ciaran
Authors: McCreesh, C., and Prosser, P.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:ACM Transactions on Parallel Computing
Publisher:Association for Computing Machinery
ISSN:2329-4949
ISSN (Online):2329-4957
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