A Progressive Search Algorithm for the Minimum Hitting Set Problem

Given a finite universe and a collection of the subsets of the universe, the minimum hitting set of the collection is the smallest subset of the universe that has non-empty intersection with each set in the collection. Finding the minimum hitting set is an NP-Hard problem that has many real world applications. In this study, we propose a progressive search-based approach to find the minimum hitting set of a given collection. The algorithm starts searching for the hitting sets of size 1 and increase the expected size of the minimum hitting set by a factor of d. After each unsuccessful search, it increases the expected size by d and generate the candidate sets with the expected size. After each successful search, the algorithm takes the average of last unsuccessful and successful searches and continue the searching with the new expected size. The algorithm terminates when the detected upper bound coincides with the detected lower bound. The effect of different values for d on the performance of the algorithm has been experimented on various data sets. Experimental results reveal that the proposed method effectively computes the minimum hitting set on real-world data and random dataset.