Multiplicative Weights Update Analysis of Set Multicover
集合多覆盖问题的乘性权重更新分析

The simple greedy algorithm for set multicover has approximation ratio.This paper presents a variation of the simple greedy algorithm,Breadth First Greedy Algorithm,and proves its approximation ratio can be (In n)/r lnlnn O(1),where r is the cover requirement.This result is better than the approximation ratio O((ln n)/r ((lnn)/r))~(1/2) 1 obtained by randomized rounding method.The design of this algorithm fits in the framework of multi- plicative weights update method,proposed by Arora etc.recently.