## 1 Introduction  
Lossy link refers to the link which frequently loses packets. With the maturing of wireless sensor network technology, the practical application system of wireless sensor networks gradually appears in many fields, such as environmental monitoring, data collection, _etc._ Network congestion, too low energy of nodes or wireless communication interferences in wireless sensor networks will result in the loss of severe packets upon linking. Lossy link seriously affects the performance of wireless sensor networks, so it must be found and repaired.  
The detecting technology of lossy links is divided into two types: measurement based on collaborative internal nodes and that based on end-to-end nodes. The measurement based on collaborative internal nodes requires each internal node to monitor the packets loss rate of its adjacency link and report it to the sink node. It is straightforward but results in a huge traffic burden, so it is not suitable for wireless sensor networks of limited resources. Each deployed sensor network faces one or some certain applications, in which the node sends application data to the sink node regularly. The technology to infer the performance of links using end-to-end measurement data is called Network Tomography (NT) technology [1]. The advantage of end-to-end measurement is that it does not generate extra monitoring traffic, and this passive measurement does not need extra consumption energy of nodes. Packets loss of application data onto sensor nodes to sink nodes is measured passively using the measurement, and lossy link is inferred using Network Tomography.  
Network Tomography currently used to infer lossy links is divided into two types: probing correlations between data packets and scanning single fault. The method of probing correlations between data packets needs to make sure that there are strict correlations between probe packets. [PERSON] and [PERSON] [2] propose that a data collection framework based on data fusion is used to make sure there are correlations between data packets. The method can infer the specific packets loss rate of each link. The method is highly accurate but is difficult to deploy, so the scope of its application is restricted. The method of scanning single faults is mainly used to infer the nature of networks which have a Boolean characteristic, such as network connectivity, lossy link, _etc._ It assumes there are a few link failures of networks, which lead to packets loss, and do not need correlations between data packets, so it is simple [3]. [PERSON] _et al._[4] propose a Linear Programming (LP) algorithm and Bayesian inference algorithm based on Gibbs sampling. [PERSON] [5,6] proposes a SCFS inference algorithm based on a greedy strategy. [PERSON] sampling algorithms have the highest accuracy, but are difficult to apply in inference computation in large-scale network because of high computational cost. SCFS algorithm is simple and its computing speed is very fast, but it tends to give priority to select the links closed to root nodes as lossy links, so it has a big error and can only be used for tree topology. Based on the above research, this paper proposes a heuristic algorithm to infer lossy links, mapping the problem of lossy link inferences to minimal set-cover problems.