Deriving All Minimal Hitting Sets Based on Join Relation

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 45; no. 7; pp. 1063 - 1076
• Main Authors: Xiangfu Zhao, Dantong Ouyang
• Format: Journal Article
• Language: English
• Published: IEEE 01.07.2015
• Subjects: Arrays; Benchmark testing; Complexity theory; Cybernetics; Distribution; equivalence relation; hitting set; incremental diagnosis; join relation; Predictive models; Silicon; Tin; hitting set; equivalence relation; incremental diagnosis; Distribution; join relation
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2015.2400423

Deriving all minimal hitting sets (MHSes) for a family of conflict sets is a classical problem in model-based diagnosis. A technique for distributed MHSes based on the join relation of elements is proposed. Then, a strategy for deriving all distributed MHSes is presented. If the family of sets is decomposed into a number of equivalence classes based on the join relation, then parallel computation of MHSes for each distribution can be applied. Moreover, an incremental, distributed approach is introduced. When a new conflict set is added, only related distributed MHSes are chosen to incrementally update the final result. From a theoretical point of view, the complexity of the distributed algorithm is O(2 num/k ), while the complexity of the corresponding centralized algorithm is O(2 num ), with k and num being the number of equivalence classes and the number of basic elements in all the conflict sets, respectively. Furthermore, compared with the corresponding centralized approach, a large number of set-containment checks are avoided by the incremental, distributed approach. Experimental results, including both numerous artificial examples and typical International Symposium on Circuits and Systems-85 benchmark circuit conflict set examples, offer evidence that, compared with centralized methods, the efficiency for deriving all MHSes in a distributed (incremental) way is considerably improved.