Parallel computation of the minimal elements of a poset

Authors:
Charles E. Leiserson;Marc Moreno Maza;Liyun Li;Yuzhen Xie
Affiliations:
Massachusetts Institute of Technology, Cambridge, MA;University of Western Ontario, London, ON, Canada;University of Western Ontario, London, ON, Canada;University of Western Ontario, London ON, Canada
Venue:
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Year:
2010

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Abstract

Computing the minimal elements of a partially ordered finite set (poset) is a fundamental problem in combinatorics with numerous applications such as polynomial expression optimization, transversal hypergraph generation and redundant component removal, to name a few. We propose a divide-and-conquer algorithm which is not only cache-oblivious but also can be parallelized free of determinacy races. We have implemented it in Cilk++ targeting multicores. For our test problems of sufficiently large input size our code demonstrates a linear speedup on 32 cores.