Bing Wang, Wei Wei, Hieu Dinh, Wei Zeng, Krishna R. Pattipati (Fellow IEEE) IEEE Transactions on Mobile Computing, March 2012 Introduction Problem Setting and Goal Optimal Sequential Testing Heuristic Sequential Testing Schemes Ordering Algorithm Greedy Algorithm Performance Evaluation Conclusions Wireless sensor networks have been deployed in a wide range of applications. A deployed sensor network may suffer from many network-related faults, e.g., malfunctioning or lossy nodes or links. These faults affect the normal operation of the network, and hence should be detected localized and corrected/repairs. Two categories exist in literature Active Measurement Passive Measurement Active Measurement A node needs to monitor itself or its neighbors, and transmit the monitoring results locally or to a centralized server. Advantages Exactly pinpoint the faults. Drawback Consume precious resources of sensor nodes Reduce the lifetime of the network. Passive Measurement Uses existing end-to-end data inside networks: if end-to-end data indicate faulty end-to-end behaviors, then some components in the network must be faulty. Advantage No additional traffic into the network Drawback It poses the challenge of fault inference-accurate inference from end-to-end data. Motivated by the complementary strengths of active and passive measurements, the authors propose an approach Using active measurement to resolve ambiguity in passive measurements Using passive measurement to guide active measurements to reduce expected testing cost Consider a sensor network where sensed data are sent from sources to a sink. The amount of end-to-end data can be used to detect faults in the network. The goal of this paper is to localize persistently lossy links that are used in routing. The status of a component can be tested through active measurements. The test incurs a testing cost The personnel wages when human is involved The resources used at a sensor node to monitor itself and neighboring nodes/links The energy and network bandwidths used to transfer the monitoring results to the sink A link is lossy or not based on its average loss rate or reception rate. The threshold, t l, can clearly separate good and bad links. Complete path information Know the path used by a source at any point of time Probabilistic path information Only know the set of paths that are used by a source and the probability using each path The authors define path reception rate as the probability that a packet traverses a path successfully. When n data packets are transmitted along a path and m packets are received successfully, the path reception rate is estimated as m/n. Using end-to-end data, we have narrowed down the potential lossy links to the set of links that are used by bad paths/pairs, excluding those used by good paths/pairs. Testing cost An optimal solution to the sequential testing problem is one that leads to the minimum expected total test cost The goal of this paper To minimize expected testing cost The authors also proved the sequential testing problem is NP-hard problem. For a given instance of the optimal sequential testing problem, I The recursive equation: the minimum expected testing cost the testing cost of link l k the prior probability that link l k is lossy I kb is the resultant instance when l k is found to be lossy I kg is the resultant instance when l k is found to be good P1P1 P2P2 Expected testing cost: c 1 P1P1 P2P2 Expected testing cost: c 3 + (1-p 3 )*(c 1 + c 2 ) Two heuristic schemes are proposed in this paper. Ordering Algorithm Greedy Algorithm In each step, this algorithm picks the link with the highest n k p k /c k to test, where n k is the number of paths that use link l k 4 paths: P 1 =(l 2, l 1 ) P 2 =(l 3, l 1 ) P 3 =(l 4, l 1 ) P 4 =(l 5 ) If we know complete path information l 1, l 2, l 3, l 4 l1l1 l 2, l 3, l 4 l1l1 G B nkpk/cknkpk/ck If we know probabilistic path information 3 bad pairs: P 1 =(l 2, l 1 ) P 2 =(l 3, l 1 ) P 3 =(l 4, l 1, l 5 ) In each step, this algorithm picks the link that provides the highest gain. The gain from knowing the status of a link is defined as the cost savings subtracted by the testing cost of this link. If we know the complete path information 4 paths: P 1 =(l 2, l 1 ) P 2 =(l 3, l 1 ) P 3 =(l 4, l 1 ) P 4 =(l 5 ) If we know the probabilistic path information 3 bad pairs: P 1 =(l 2, l 1 ) P 2 =(l 3, l 1 ) P 3 =(l 4, l 1, l 5 ) The complexity of the ordering algorithm is O(| L | 2 | P |) The complexity of the greedy algorithm is O(| L | 3 | P |) In some special topology cases, the greedy scheme leads to optimal solutions while the greedy scheme may not. The network is deployed in a 10unit X 10unit square. A single sink is deployed at the center. 500 nodes are deployed in the square. The transmission range of each node is 3 units. At a given point of time, the paths from the sources to the sink form a reversed tree. The exhaustive inspection approach infers in parallel a set of potential faulty components from end-to-end measurements, tests each identified component, and repairs the faulty ones at the end of the iteration. The authors formulated an optimal sequential testing problem that carefully combines active and passive measurements for fault localization in WSN. The authors proposed a recursive approach and two heuristic algorithms to solve it.