MHS2: A Map-Reduce Heuristic-Driven Minimal Hitting Set Search Algorithm
Computing minimal hitting sets (also known as set covers) for a collection of sets is an important problem in many domains (e.g., model/reasoning-based fault diagnosis). Being an NP-Hard problem, exhaustive algorithms are usually prohibitive for real-world, often large, problems. In practice, the usage of heuristic based approaches trade-off completeness for time efficiency. An example of such heuristic approaches is Staccato, which was proposed in the context of reasoning-based fault localization. In this paper, we propose an efficient distributed algorithm, dubbed MHS2, that renders the sequential search algorithm Staccato suitable to distributed, Map-Reduce environments. The results show that MHS2 scales to larger systems (when compared to Staccato), while entailing either marginal or small runtime overhead.
KeywordsMinimal Hitting Set Map-Reduce Distributed Computing
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- 1.Abreu, R., van Gemund, A.J.C.: A low-cost approximate minimal hitting set algorithm and its application to model-based diagnosis. In: Symposium on Abstraction, Reformulation, and Approximation, SARA 2009 (2009)Google Scholar
- 2.Abreu, R., Zoeteweij, P., van Gemund, A.J.C.: On the accuracy of spectrum-based fault localization. In: Testing: Academic and Industrial Conference Practice and Research Techniques, TAICPART 2007 (2007)Google Scholar
- 3.de Kleer, J., Williams, B.C.: Readings in model-based diagnosis (1992)Google Scholar
- 4.Dean, J., Ghemawat, S.: Mapreduce: simplified data processing on large clusters. In: Symposium on Opearting Systems Design & Implementation, OSDI 2004 (2004)Google Scholar
- 5.Feldman, A., Provan, G., Van Gemund, A.: Computing minimal diagnoses by greedy stochastic search. In: AAAI Conference on Artificial intelligence, AAAI 2008 (2008)Google Scholar
- 6.Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness (1990)Google Scholar
- 7.Harrold, M.J., Rothermel, G., Wu, R., Yi, L.: An empirical investigation of program spectra. In: Program Analysis for Software Tools and Engineering, PASTE 1998 (1998)Google Scholar
- 8.Pill, I., Quaritsch, T.: Optimizations for the boolean approach to computing minimal hitting sets. In: European Conference on Artificial Intelligence, ECAI 2012 (2012)Google Scholar
- 9.Reiter, R.: A theory of diagnosis from first principles. Artificial Intelligence 32(1) (1987)Google Scholar
- 10.Rubin, J.: A Technique for the Solution of Massive Set Covering Problems, with Application to Airline Crew Scheduling (1973)Google Scholar
- 11.Ruchkys, D.P., Song, S.W.: A parallel approximation hitting set algorithm for gene expression analysis. In: Symposium on Computer Architecture and High Performance Computing (2002)Google Scholar
- 12.Wotawa, F.: A variant of Reiter’s hitting-set algorithm. Information Processing Letters 79(1) (2001)Google Scholar