Practical Algorithms for Finding Extremal Sets
Martin Marinov, Nicholas Nash, David Gregg

TL;DR
This paper introduces two improvements to the extremal set identification algorithm AMS-Lex, using memoization and parallelization, resulting in significantly faster execution times on various datasets, including real-world and synthetic data.
Contribution
The paper presents novel memoization and parallelization techniques that substantially enhance the efficiency of the AMS-Lex algorithm for finding extremal sets.
Findings
Memoization improves execution time by over 400 times in some cases.
Multi-threaded implementation outperforms original AMS-Lex by 3 to 6 times.
Parallel CPU implementation matches GPU-based performance on synthetic datasets.
Abstract
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, \textit{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 times faster than the highly efficient publicly available implementation of AMS-Lex. Moreover, we show that our…
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Taxonomy
TopicsBayesian Modeling and Causal Inference · Complexity and Algorithms in Graphs · Advanced Graph Theory Research
