A Tighter Analysis of Setcover Greedy Algorithm for Test Set

Setcover greedy algorithm is a natural approximation algorithm for test set problem. This paper gives a precise and tighter analysis of performance guarantee of this algorithm. The author improves the performance guarantee $2\ln n$ which derives from set cover problem to $1.1354\ln n$ by applying the potential function technique. In addition, the author gives a nontrivial lower bound $1.0004609\ln n$ of performance guarantee of this algorithm. This lower bound, together with the matching bound of information content heuristic, confirms the fact information content heuristic is slightly better than setcover greedy algorithm in worst case.