The Minimal Hitting Set Generation Problem: Algorithms and Computation

Abstract

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.

MCS2: Minimal coordinated supports for fast enumeration of minimal cut sets in metabolic networks

“…At the moment, the main approach used for enumerating the MCSs for a target reaction is to compute the elementary flux modes containing the target and then use a dualization procedure to produce the MCSs [GDVL17]. Here, flux modes are possible distributions of fluxes through the reactions, and those can be modelled as hyperedges on the vertex set of possible reactions.…”

A hybrid CPU‐GPU‐MIC algorithm for minimal hitting set enumeration

“…Table shows the processing time of our MHS enumeration algorithm for the HER2+ SHORT dataset for cardinalities k ∈ {5,7,10}. For cardinalities 5 and 7, our algorithm kept reasonable performances when compared to other algorithms of the literature. The noteworthy result is for k = 10.…”

“…Although closely related to HSP, the MHS enumeration problem remains with its complexity unknown, so far only non polynomial‐time algorithms are known and it is a notorious open problem to find polynomial‐time algorithms to solve it. Gainer‐Dewar and Vera‐Licona present an extensive review of recent MHS enumeration algorithms.…”

“…The common point of all of these categories and their algorithms is that, although these algorithms provide clever approaches to enumerate MHSs, they are either sequential with procedures that are hard to parallelize, or multithreaded parallel with no aid of accelerator devices (notably GPUs and/or MICs), and with procedures that lead to memory exhaustion even for medium sized MHS instances.…”

Multi-hop Byzantine reliable broadcast with honest dealer made practical

“…We made use of the implementation provided by Gainer-Dewar and Vera-Licona [10] for the algorithm defined by Murakami and Uno [21] to solve the VC reduction to the hitting set problem.…”