LinearMerge: Efficient computation of minimal hitting sets for conflict sets in a linear structure

The efficient generation of minimal hitting sets (MHSs) for large conflict sets is an important topic for classical model-based diagnosis. To date, the structures of conflict sets have not been taken into account for computing MHSs by most previous methods, although they may play an important role. In this paper, a type of basic linear structure of conflict sets is described. Based on this linear structure and the classical strategy “divide and conquer”, an efficient approach, that is, LinearMerge, is proposed for solving large MHS problems. In theory, compared with direct “divide and conquer” without considering the linear structure of conflict sets, LinearMerge decreases the complexity of each merge from quadratic to linear, in the product of the number of MHSs for each sub-family of conflict sets. Experimental results on regular synthetic data demonstrate that LinearMerge has higher efficiency than many other well-known approaches, and saves several orders of magnitude of time (seconds). Furthermore, many families of conflict sets for widely used ISCAS-85 benchmark circuits manifest the property of a linear structure, and more than 95% of them include sub-families in a linear structure, in some circuits. Experimental results on such benchmarks also show that LinearMerge is more efficient than other efficient approaches, and in many cases, LinearMerge saves more than 99% of the time cost.