On LP-relaxation Approximation of Minimum Test Set
关于最小测试集的线性规划松弛近似

The up-to-date best approximation ratio of minimum test set is 21nn+o(1)of the greedy algorithm. It is an open problem if this approximation ratio can be improved. This paper discusses the ability of the methods for proof of the approximation ratios based on the LP-relaxation. We prove the integrality gap of minimum test set is at least 0.72 In n and the coefficient of the integrality gap of minimum test set can be as large as that of minimum set cover. Moreo- ver, we show one cannot improve the approximation ratio of the greedy algorithm for weighted minimum test set by more than a constant.