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Traffic flow measurement is of great importance to ISPs for various network engineering tasks. An interesting problem is that how to determine the minimum number of links by monitoring which one can obtain the traffic flows of the whole ISP network. Previous works view the problem as Vertex Cover problem. They suffer from high time complexity and redundant monitoring. Different from these works, we study the problem from the perspective of edges and propose two models. The first model, Extended Edge Cover model, can determine the minimum set of monitored links, which are 30% less than that of previous works. The second model, shared-path model, is more suitable when the monitoring resources are limited but one still wants to measure a large part of the networks. Using this method, one can measure 85% of the network by monitoring 5% of links. Finally, we evaluate the performance of the two models through extensive simulations. The experimental results show the effectiveness and robustness of the two models.