After the embargo period via non-commercial hosting platforms such as their institutional repository  via commercial sites with which Elsevier has an agreement In all cases accepted manuscripts should: link to the formal publication via its DOI  bear a CC-BY-NC-ND licensethis is easy to do  if aggregated with other manuscripts, for example in a repository or other site, be shared in alignment with our hosting policy  not be added to or enhanced in any way to appear more like, or to substitute for, the published journal article

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Given a public transportation network of stations and connections, we want to find a minimum subset of stations such that each connection runs through a selected station. Although this problem is NP-hard in general, real-world instances are regularly solved almost completely by a set of simple reduction rules. To explain this behavior, we view transportation networks as hitting set instances and identify two characteristic properties, locality and heterogeneity. We then devise a randomized model to generate hitting set instances with adjustable properties. While the heterogeneity does influence the effectiveness of the reduction rules, the generated instances show that locality is the significant factor. Beyond that, we prove that the effectiveness of the reduction rules is independent of the underlying graph structure. Finally, we show that high locality is also prevalent in instances from other domains, facilitating a fast computation of minimum hitting sets.

We devise an enumeration method for inclusion-wise minimal hitting sets in hypergraphs. It has delay O(m k * +1 • n 2 ) 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.

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After the embargo period via non-commercial hosting platforms such as their institutional repository  via commercial sites with which Elsevier has an agreement In all cases accepted manuscripts should: link to the formal publication via its DOI  bear a CC-BY-NC-ND licensethis is easy to do  if aggregated with other manuscripts, for example in a repository or other site, be shared in alignment with our hosting policy  not be added to or enhanced in any way to appear more like, or to substitute for, the published journal article