关于最小测试集的线性规划松弛近似  

On LP-relaxation Approximation of Minimum Test Set

作　　者：崔鹏[1] 刘红静[2] 

机构地区：[1]中国人民大学信息资源管理学院,北京100871 [2]保定市财贸学校,保定071000

出　　处：《计算机科学》2005年第10期157-159,166,共4页Computer Science

摘　　要：目前最小测试集的最佳近似比是贪心算法的2lnn-o(1)。这个近似比能否改进是一个公开的问题。本文讨论了最小测试集的基于线性规划松弛的近似比证明方法的能力问题。我们证明最小测试集的整性间隙至少为0.72lnn,而且最小测试集整性间隙的系数可以与最小集合覆盖的整性间隙的系数一样大。另外,我们说明加权最小测试集的贪心算法的近似比不能通过对偶拟合方法改进超过一个常数。The up-to-date best approximation ratio of minimum test set is 2ln n＋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 ln n and the coefficient of the integrality gap of minimum test set can be as large as that of minimum set cover. Moreover, we show one cannot improve the approximation ratio of the greedy algorithm for weighted minimum test set by more than a constant.

关 键 词：最小测试集 贪心算法 整性间隙 对偶拟合 线性规划松弛 测试集 近似比 最小 贪心算法 证明方法 集合覆盖 拟合方法 间隙 

分 类 号：TP393[自动化与计算机技术—计算机应用技术] O211.1[自动化与计算机技术—计算机科学与技术]