Enumeration of Minimal Hitting Sets Parameterized by Treewidth

TL;DR

This paper presents an improved fixed-parameter-linear delay algorithm for enumerating minimal hitting sets in hypergraphs, with complexity depending on the treewidth, advancing the efficiency of related data management tasks.

Contribution

It introduces a fixed-parameter-linear delay enumeration algorithm for minimal hitting sets parameterized by treewidth, with an FPT preprocessing phase and exponential memory in treewidth.

Findings

Achieves fixed-parameter-linear delay in enumeration

Preprocessing phase depends on treewidth

Memory usage is exponential in treewidth

Abstract

Enumerating the minimal hitting sets of a hypergraph is a problem which arises in many data management applications that include constraint mining, discovering unique column combinations, and enumerating database repairs. Previously, Eiter et al. showed that the minimal hitting sets of an $n$-vertex hypergraph, with treewidth $w$, can be enumerated with delay $O^*(n^{w})$ (ignoring polynomial factors), with space requirements that scale with the output size. We improve this to fixed-parameter-linear delay, following an FPT preprocessing phase. The memory consumption of our algorithm is exponential with respect to the treewidth of the hypergraph.