Abstract
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 analyzed based on the maximal flow partition.
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