集合多覆盖问题的乘性权重更新分析

集合多覆盖问题的简单贪心算法的近似比是lnn＋1。本文提出简单贪心算法的一个变形，宽度优先贪心算法，并且证明其有近似比（lnn）／r＋lnlnn＋O（1），其中r是覆盖要求。这个结果比由随机取整方法得到的近似比O（（lnn）/r＋√（lnn）＋1为优。宽度优先贪心算法的设计可以归入Arora等最近提出的乘性权重更新方法的框架。关键词集合多覆盖，宽度优先贪心算法，乘性权重更新方法

Multiplicative Weights Update Analysis of Set Multicover

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.