An Efficient Branch-and-Bound Solver for Hitting Set

TL;DR

This paper introduces a branch-and-bound algorithm for the hitting set problem that, despite its exponential worst-case complexity, efficiently solves many practical instances and outperforms existing ILP solvers.

Contribution

The paper presents a novel branch-and-bound method specifically optimized for hitting set, significantly improving practical solving times over current ILP approaches.

Findings

Outperforms modern ILP solvers by at least an order of magnitude on most instances

Efficiently solves many practical hitting set instances despite exponential worst-case complexity

Demonstrates effectiveness across diverse application domains

Abstract

The hitting set problem asks for a collection of sets over a universe $U$ to find a minimum subset of $U$ that intersects each of the given sets. It is NP-hard and equivalent to the problem set cover. We give a branch-and-bound algorithm to solve hitting set. Though it requires exponential time in the worst case, it can solve many practical instances from different domains in reasonable time. Our algorithm outperforms a modern ILP solver, the state-of-the-art for hitting set, by at least an order of magnitude on most instances.