Practical Algorithms for Finding Extremal Sets

Martin Marinov, Nicholas Nash, David Gregg
arXiv:1508.01753 [cs.DS], (7 Aug 2015)


   title={Practical Algorithms for Finding Extremal Sets},

   author={Marinov, Martin and Nash, Nicholas and Gregg, David},






The minimal sets within a collection of sets are defined as the ones which do not have a proper subset within the collection, and the maximal sets are the ones which do not have a proper superset within the collection. Identifying extremal sets is a fundamental problem with a wide-range of applications in SAT solvers, data-mining and social network analysis. In this paper, we present two novel improvements of the high-quality extremal set identification algorithm, AMS-Lex, described by Bayardo and Panda. The first technique uses memoization to improve the execution time of the single-threaded variant of the AMS-Lex, whilst our second improvement uses parallel programming methods. In a subset of the presented experiments our memoized algorithm executes more than 400 times faster than the highly efficient publicly available implementation of AMS-Lex. Moreover, we show that our modified algorithm’s speedup is not bounded above by a constant and that it increases as the length of the common prefixes in successive input itemsets increases. We provide experimental results using both real-world and synthetic data sets, and show our multi-threaded variant algorithm out-performing AMS-Lex by 3 to 6 times. We find that on synthetic input datasets when executed using 16 CPU cores of a 32-core machine, our multi-threaded program executes about as fast as the state of the art parallel GPU-based program using an NVIDIA GTX 580 graphics processing unit.
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