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The Boolean approach to computing minimal hitting sets proposed by Lin and Jiang is known to offer very attractive general performance, but also has its issues, specifically with a cardinality-restricted search. In this paper we propose optimizations regarding the refinement rules, also offering a revised decision strategy as well as optimized termination criteria that exploit cardinality bounds. Our experiments including artificial and real-world samples for the bounded and unbounded case show the potential of our work, where we could achieve speed-ups of up to two orders of magnitude.
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