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MHS generation algorithms

This repository contains a collection of implemented algorithms for solving the Minimal Hitting Set generation problem. We provide easy-to-use AlgoRun containers for these algorithms, so you don't have to worry about compiling anything.

The minimal hitting set generation problem

Consider a family H of sets E₁, E₂, … En. A hitting set of H is a set S with the property that S intersects every one of the Es. A minimal hitting set is a hitting set which cannot be made smaller without losing this property. The minimal hitting set generation problem is to compute all the minimal hitting sets of the given family H.

For example, suppose that H is [[1, 2, 5], [2, 3, 4], [1, 3]]. Then [1, 2, 3] is a hitting set, because every set in H has at least one of these elements. However, it is not a minimal hitting set, because we could remove either 2 or 3! [1, 2] and [1, 3] are both minimal hitting sets of H.

Minimal hitting sets are important in a wide array of applications, ranging from very abstract mathematics (Boolean algebra and hypergraph theory) to high-tech applications (computational biology and data mining). Hitting sets have even been used to prove that there is no 16-clue sudoku! As a result, many algorithms have been developed to generate minimal hitting sets.

The containers

However, researchers in different domains are not always aware of the large literature on the subject, and so highly-performant algorithms from one domain may not be used by researchers in another. In addition, the existing survey literature tends to focus on the problem of recognizing the collection of minimal hitting sets (rather than generating it), and much attention is dedicated to asymptotic and worst-case analysis rather than practical performance.

To help the researcher who wants to actually compute MHSes from real data, we have assembled a collection of software implementations of seventeen algorithms which reflect the long history and remarkable breadth of research in this area. You can read more about the algorithms in the containers README and about running them in the AlgoRun README.

Each of these software packages is wrapped in a Docker container based on the AlgoRun framework. You can easily download and run these containers yourself! For more information about how to do this (either to test the algorithms on your own inputs or to integrate the algorithms into your research), consult the HOWTO.

Benchmark inputs

A variety of example inputs are provided in the benchmark_inputs folder. Check the file for more information about these data sets.

Benchmark results

We have performed a number of performance benchmarks on all of the algorithms using the provided inputs. The results are included in the results directory. For further information, see our paper.


Code in this repository is distributed under a mixture of licenses. See each file for details. (In particular, code written by AGD for this project is typically released under the GPL 3.0, while upstream algorithm code is distributed under a variety of licenses.)


This repository is a project of the Vera-Licona Research Group and was assembled by Andrew Gainer-Dewar.

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