Efficient and Effective Practical Algorithms for the Set-Covering Problem

The set-covering problem is an interesting problem in computational complexity theory. In [1], the setcovering problem has been proved to be NP hard and a greedy heuristic algorithm is presented to solve the problem. In [2], the set-covering problem is found to be equivalent to the problem of identifying redundant search engines on the Web, and finding efficient and effective practical algorithms to the problem becomes a key issue in building a vary large-scale Web meta-search engine. A new algorithm Check-And-Remove (CAR) is proposed in [2] with a better time complexity than the greedy algorithm presented in [1]. However, in some cases the cover set produced by the new algorithm is too large to be acceptable. We propose some changes to the data structure that improve the performance of both algorithms. We also present a new greedy algorithm whose time complexity is the same as that of the CAR algorithm. The experimental results show that our final greedy algorithm runs faster than the CAR algorithm and produces better results in all test cases.