  Finding inclusion-minimal "hitting sets" for a given collection of sets is a
fundamental combinatorial problem with applications in domains as diverse as
Boolean algebra, computational biology, and data mining. Much of the
algorithmic literature focuses on the problem of *recognizing* the collection
of minimal hitting sets; however, in many of the applications, it is more
important to *generate* these hitting sets. We survey twenty algorithms from
across a variety of domains, considering their history, classification, useful
features, and computational performance on a variety of synthetic and
real-world inputs. We also provide a suite of implementations of these
algorithms with a ready-to-use, platform-agnostic interface based on Docker
containers and the AlgoRun framework, so that interested computational
scientists can easily perform similar tests with inputs from their own research
areas on their own computers or through a convenient Web interface.
