Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling

Blasius, T., Friedrich, T., Lischeid, J., Meeks, K. and Schirneck, M. (2019) Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling. In: 21st Workshop on Algorithm Engineering and Experiments (ALENEX 2019), San Diego, CA, USA, 7-8 Jan 2019, ISBN 9781611975499 (doi: 10.1137/1.9781611975499.11)

Abstract

We devise an enumeration method for inclusion-wise minimal hitting sets in hypergraphs. It has delay O(mk* +1 · n2) and uses linear space. Hereby, n is the number of vertices, m the number of hyperedges, and k* the rank of the transversal hypergraph. In particular, on classes of hypergraphs for which the cardinality k* of the largest minimal hitting set is bounded, the delay is polynomial. The algorithm solves the extension problem for minimal hitting sets as a subroutine. We show that the extension problem is W[3]-complete when parameterised by the cardinality of the set which is to be extended. For the subroutine, we give an algorithm that is optimal under the exponential time hypothesis. Despite these lower bounds, we provide empirical evidence showing that the enumeration outperforms the theoretical worst-case guarantee on hypergraphs arising in the profiling of relational databases, namely, in the detection of unique column combinations.

• Item Type: Conference Proceedings
• Additional Information: The fourth author is supported by a Personal Research Fellowship of the Royal Society of Edinburgh, funded by the Scottish Government.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Meeks, Dr Kitty
• Authors: Blasius, T., Friedrich, T., Lischeid, J., Meeks, K., and Schirneck, M.
• College/School: College of Science and Engineering > School of Computing Science
• ISBN: 9781611975499
• Copyright Holders: Copyright © 2019 by SIAM
• Publisher Policy: Reproduced in accordance with the publisher copyright policy