A Low-Cost Approximate Minimal Hitting Set Algorithm and its Application to Model-Based Diagnosis

Generating minimal hitting sets of a collection of sets is known to be NP-hard, necessitating heuristic approaches to handle large problems. In this paper a low-cost, approximate minimal hitting set (MHS) algorithm, coined STACCATO, is presented. STACCATO uses a heuristic function, borrowed from a lightweight, statistics-based software fault localization approach, to guide the MHS search. Given the nature of the heuristic function, STACCATO is specially tailored to model-based diagnosis problems (where each MHS solution is a diagnosis to the problem), although well-suited for other application domains as well. We apply STACCATO in the context of model-based diagnosis and show that even for small problems our approach is orders of magnitude faster than the brute-force approach, while still capturing all important solutions. Furthermore, due to its low cost complexity, we also show that STACCATO is amenable to large problems including millions of variables.