Compressed Topology Tomography in Sensor Networks

1. Compressed Topology Tomography in Sensor Networks Chunnan Yao Directed by Dr.Haifeng Zheng, Dr.Su Zhang 1

2. Outline Introduction Background Objective problem model using compressive sensing Step1:reconstruction of path Step2:reconstruction of link parameters Summary&future work Compressed Topology Tomography in Sensor Networks 2 2

3. Background • WSN topology tomography • we need to know the status of parameters(such as delay)for links inside a WSN. It helps us to understand detailed properties of the network in many network maintenance and diagnosis situations. • Difficulties • WSN is self-organized and usually deployed in dynamic environments. No fixed routing path can be expected for each node. Compressed Topology Tomography in Sensor Networks 3

4. Objective • We seek to infer the status of parameters(such as delay）for links inside a network through information collected by the sink node. Compressed Topology Tomography in Sensor Networks 4

5. Problem formulation • Additive linear model represents the relationship between a measured path and an individual link delay[1]. sink n2->n6: l1->l3->l4 n1->n5: l2->l3->l5 n1->n2: l2->l1 n5->n6: l5->l4 [1]Firooz M, Roy S. Link delay estimation via expander graphs[J]. 2011. Compressed Topology Tomography in Sensor Networks 5

6. Problem formulation • x is n×1（unkown) vector of the individual link delay. R is r×n routing matrix for each packet. y is the measured r-vector by the sinking node. • Here we assume the network consisting of bidirectional links, and no looped routes exist. • For most networks, n>>r! Compressed Topology Tomography in Sensor Networks

7. Problem formulation • Basic idea: Compressive sensing[2] • standard CS framework: • X is an N×1 sparse discrete signal vector, Φis an M×N measurement matrix and Y is the M×1 measurement vector. M<<N. • This can be achieved by solving the following optimization: [2]Candès E J, Romberg J, Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. Information Theory, IEEE Transactions on, 2006, 52(2): 489-509. Compressed Topology Tomography in Sensor Networks 7

8. Problem formulation =Φ • Step1: determine the sensing matrix Φ using path reconstruction • Step2: Given all paths(Φ) and sink node information(Y), determine link properties X(delay,packet loss rate, etc). • The speed and accuracy of of step1 is vital. Compressed Topology Tomography in Sensor Networks 8

9. Outline Introduction problem model using compressive sensing Step1:reconstruction of path a state-of-art method: MNT reconstruction using CS my refinement Step2:reconstruction of link parameters Summary&future work Compressed Topology Tomography in Sensor Networks 9 9

10. MNT(Multi-hop Network Tomography • Use data already attached to each packet. • Key part: time estimation • Advantages:1. No change in the headers of inner nodes.2. Low computation complexity. • Disadvantages:1. susceptible to packet losses and routing dynamics. Default CTP header: source ID, sequence number, oder, parent node ID, hop count According to data from trace-driven simulations on Citysee, MNT's accuracy is below 60% in a certain WSN scenrio, which is not satisfactory. Compressed Topology Tomography in Sensor Networks 10

11. CS based path reconstruction • Different paths need to be classified, ie. add a header:bFlt, use an L-bit array associated with H independent hash functions) to space-efficiently record node IDs[3][4]. • The path already reconstructed are stored for future reuse. • Advantages:1. resist to dynamic links 2. lower delay • Disadvantages:1. more computation complexity on sinking node 2. packet overhead 3. Packets from inactive nodes have less opportunity to be reconstructed. [3]Xiaoyan Z, Houjun W, Zhijian D. Wireless sensor networks based on compressed sensing [4]Ideas from Dr. Haifeng Zheng Compressed Topology Tomography in Sensor Networks 11

12. My refinement • Inspiration • Wasted pre-failure information in MNT • Reconstruct the total path using CS after failure of MNT • Design of the combination • Implement path classification and introduce additional header 'Acc' to every node in the same way as that in CS reconstruction method. • However, at the sink node, we implement MNT first to get the failure point, denoded by pf. Then we use pf to get a new sensing matrix(Φ') and compressed information(y'). Solve ,in which the number of sensing matrix's row is reduced by f Compressed Topology Tomography in Sensor Networks 12

13. Simulation of Step1 • Configurations • 400 nodes(1 sink node) randomly distributed in a 1000*1000 area. Nodes in the radius of 65 can form a link. The number 65 is chosen to ensure each nodes are connected. • We simulate 40000 time units. In each time unit, 5 nodes transmit packets. Nodes are classified as 'active' and 'inactive', whose sending probability is 0.0125 and 0.001. • The routing path is formed by the shortest path algorithm. • The success rate of MNT is set as 70%, which means 30% packets' path need CS to reconstruct. Compressed Topology Tomography in Sensor Networks 13

14. Simulation result of step1 • Improvements of my refinement: • Lower loss rate. When reconstruction procedure is finished, CS based reconstruction has a loss rate of 12.15%, while CS&MNT is 6.20% • Less delay. The time when CS based method reaches its reconstruction plateau is 6459, while CS&MNT is 5433. • Higher reconstruction rate. MNT can help CS to reconstruct the paths of inactive nodes. CS based method reconstructs 88.72% paths while CS&MNT reconstructs 96.74%. Compressed Topology Tomography in Sensor Networks 14

15. Outline Introduction problem model using compressive sensing Step1:reconstruction of path Step2:reconstruction of link parameters Stasis, pre-determined network tomography Expander graph Use expander graph in WSN Summary&future work Compressed Topology Tomography in Sensor Networks 15 15

16. Step2:reconstruction of link parameters • Stasis, pre-determined network tomography[5] • don't need step1, and the topology of network can be pre-determined to ensure the CS reconstruction constrains:expander graph. • Recall the problem model: • Given routing matrix Φ, Y is known, X is unknown, we need to solve • Expander graph [5]Link Delay Estimation Via Expander Graphs( Mohammad H.Firooz, 2012) Compressed Topology Tomography in Sensor Networks 16

17. Step2:reconstruction of link parameters • Extend former problem model • Include all possible routes in our topology.N much larger and Φ more sparse. • probability of a random sparse matrix to be compatible to expander graph. For a (2, d, 1/4) expander graph, we have: Compressed Topology Tomography in Sensor Networks 17

18. Summary • I proposed a refinement on WSN path reconstruction problem based on MNT and CS. • I tried to verify that for a very sparse WSN routing matrix, l1-minimization method is reliable to reconstruct routing parameters. • future work: • Determine the MNT&CS switch point in Step1 using network informations. • Implement more reliable simulation and deploy MNT&CS method in real wireless sensor networks. Compressed Topology Tomography in Sensor Networks 18

19. References • Xiaoyan Z, Houjun W, Zhijian D. Wireless sensor networks based on compressed sensing[C]//Computer Science and Information Technology (ICCSIT), 2010 3rd IEEE International Conference on. IEEE, 2010, 9: 90-92. • Liang Y, Liu R. Compressed topology tomography in sensor networks[C]//Wireless Communications and Networking Conference (WCNC), 2013 IEEE. IEEE, 2013: 1321-1326. • Firooz M, Roy S. Link delay estimation via expander graphs[J]. 2011. • Keller M, Beutel J, Thiele L. Multi-hop network tomography: path reconstruction and per-hop arrival time estimation from partial information[C]//ACM SIGMETRICS Performance Evaluation Review. ACM, 2012, 40(1): 421-422. • Xu W, Mallada E, Tang A. Compressive sensing over graphs[C]//INFOCOM, 2011 Proceedings IEEE. IEEE, 2011: 2087-2095. • Berinde R, Indyk P. Sparse recovery using sparse random matrices[J]. preprint, 2008. Compressed Topology Tomography in Sensor Networks

20. Thank you for listening Chunnan Yao Directed by Dr.Haifeng Zheng, Dr.Su Zhang 20 Compressed Topology Tomography in Sensor Networks