中文摘要：

考虑网络节点的流守恒特性，网络流量的有效监测问题可抽象为求给定图G（KE）的最小弱顶点覆盖集的问题和基于流划分的最小弱顶点覆盖集的问题，这是NP难的问题．首先分析了弱顶点覆盖集的约束关系．并给出了问题的整数规划形式．然后利用原始对偶方法构造了求解最小弱顶点覆盖集的近似算法，并分析了算法的比界为2．进一步分析了求解基于最大流划分的最小弱顶点覆盖集的近似算法．

英文摘要：

Efficiently monitoring the network flow is important to a variety of network applications. Considering the equation of flow conservation, the problem of efficient monitoring is regarded as the problem of finding out the minimum weak vertex cover set and the minimum weak vertex cover set based on flow partition for a given graph G（V,E） which are all proved NP-Complete. Firstly the constraints of weak vertex cover set are analyzed and the integer programming formulation for it is given. Next an approximation algorithm for the minimum weak vertex cover set problem is constructed and the approximation ratio of 2 by primal-dual method is analyzed. Finally the approximation algorithm for the minimum weak vertex cover set is analvzad based on the maximal flow partition.