Exposure in Wireless Ad-hoc Sensor Networks

1. Exposure in Wireless Ad-hoc Sensor Networks EE206A CLASS PRESENTATION Saurabh Ganeriwal Ram Kumar

2. Wireless Sensor Network • Sensor network consists of autonomous sensor nodes • Functionality • Detect events • Relay information to the user • Applications: monitoring of wildlife, intruders, machine conditions, earthquakes, fire, contaminants etc. event sensor network

3. Technology Perspective Networkdevices tocoordinate and perform higher-level tasks Embednumerous distributed devices to monitor and interact with physical world Embedded Networked Control system w/ Small form factor Untethered nodes Exploitcollaborative Sensing, action Sensing Tightly coupled to physical world Enable spatially and temporally monitoring

4. In-node processing Wireless communication with neighboring nodes Event detection Acoustic, seismic, magnetic, etc. interface Electro-magnetic interface sensors radio CPU Limited battery supply battery Sensor Node

5. Technical Challenges • Energy Constraints • Topology management • Self Configuring • Localization, Time Synchronization etc. • Scaling • Collective behavior of nodes is what matters! • Need for a paradigm shift towards network level optimization • And so on……….

6. What is coverage ? • Given: • Field A • N sensors, specified by coordinates • How well can the field be observed ? • Measure of QoS of sensor network Good Coverage Bad Coverage

7. Problem Formulation • Given: • Initial location (I) of an agent • Final location (F) of an agent • Find: • Maximal Breach Path: • Path along which the probability of detection is minimum • Represents worst case coverage • Maximal Support Path: • Path along which the probability of detection is maximum • Represents best case coverage

8. Assumptions • Sensing Model • S(s,p) =  / [d(s,p)]k • Sensing effectiveness diminishes as distance increases (monotonic) • Homogeneous sensor nodes • Non-directional sensing technology • Centralized computation model

9. Maximal Breach • Given: Field A instrumented with sensors; areas I and F. • Problem: Identify PB, the maximal breach path in S, starting in I and ending in F. • PB is defined as a path with the property that for any point p on the path PB, the distance from p to the closest sensor is maximized.

10. Enabling Step: Voronoi Diagram By construction, each line-segment maximizes distance from the nearest point (sensor). Consequence: Path of Maximal Breach of Surveillance in the sensor field lies on the Voronoi diagram lines.

11. Graph Theoretic Formulation Given: Voronoi diagram D with vertex set V and line segment set L and sensors S Construct graph G(N,E): • Each vertex viV corresponds to a node ni N • Each line segment li Lcorresponds to an edge eiE • Each edge eiE, Weight(ei) = Distance of li from closest sensor skS Formulation: Is there a path from I to F which uses no edge of weight less than K?

12. Finding Maximal Breach Path Algorithm • Generate Voronoi Diagram • Apply Graph-Theoretic Abstraction • Search for PB Check existence of path I --> F using BFS Search for path with edge weights greater than breach weight This is a Maximal Breach Path Polynomial Time Complexity

13. Maximal Support • Given: Field A instrumented with sensors; areas I and F. • Problem: Identify PS, the maximal support path in S, starting in I and ending in F. • PS is defined as a path with the property that for any point p on the path PS , the distance from p to the closest sensor is minimized.

14. Maximal Support Given: Delaunay Triangulation of the sensor nodes Construct graph G(N,E): The graph is dual to the Voronoi graph previously described Formulation: what is the path from which the agent can best be observed while moving from I to F? (The path is embedded in the Delaunay graph of the sensors) Solution: Similar to the max breach algorithm, use BFS and Binary Search to find the shortest path on the Delaunay graph.

15. Simulation Result: Critical Regions For both breach and support, lower values of breach_weight and support_weight indicate better coverage

16. Exposure Problem • Measure of how well a moving object can be observed over a period of time, on a specific path F Maximal breach path I S Minimum exposure path Catch ! Both path length and sensing intensity should be considered.

17. Assumptions: Intensity models Effective sensing intensity at point p in field F : All Sensors Closest Sensor

18. Definition: Exposure The Exposure for an object O in the sensor field during the interval [t1,t2]along the path p(t) is:

19. Problem Formulation Given: • Field A • N sensors • Initial and final points I and F Problem: Find the Minimal Exposure Path PminE in A, starting in I and ending in F.

20. Special case: One sensor Q(0,1) P(1,0) S(0,0) Lemma: Given a sensor s and two points p and q, such that d(s,p) = d(s,q), then the minimum exposure path between p and q is the arc that is the part of the circle centered at s and passing through p and q. Can be extended to a scenario where sensor is inside a polygon

21. General exposure computations • Analytically intractable. • Need efficient and scalable methods to approximate exposure integrals and search for Minimal Exposure Paths. • Use a grid-based approach and numerical methods to approximate Exposure integrals. • Use existing efficient graph search algorithms to find Minimal Exposure Paths.

22. Generalized Grid Generalized Grid – 1st order, 2nd order, 3rd order … More movement freedom  more accurate results Approximation quality improves by increasing grid divisionswith higher costs of storage and run-time.

23. Minimal Exposure Path Algorithm • Use a grid to approximate path exposures. • The exposure (weight) along each edge of the grid approximated using numerical techniques. • Use Dijkstra’s Single-Source Shortest Path Algorithm on the weighted graph (grid) to find the Minimal Exposure Path.

24. PminE – Uniform Random Deployment Minimal exposure path for 50 randomly deployed sensors using the All-Sensor intensity model (IA). 8x8 m=1 Exposure: 0.7079 Length: 1633.9 16x16 m=2 Exposure: 0.6976 Length: 1607.7 32x32 m=8 Exposure: 0.6945 Length: 1581.0

25. Distributed algorithm for Exposure calculation

26. Localized distributed algorithm • Specialized distributed algorithms • Request and process data locally • Involve only the nodes likely to contribute to final solution • Why is it suited for sensor networks ? • Energy consumption is minimized • Less emphasis on completely accurate results • Security issues

27. Generic localized optimization procedure Initiate search Request information from neighbors /* Data Acquisition */ While (termination criteria = NO) { /* Termination rule */ Form partial solution /* Optimization mechanisms */ Decide which nodes to contact /* Search expansion rule */ Decide which nodes to terminate /* Bounding condition */ Contact selected nodes }

28. Field partitioning • Voronoi Partitioning • Advantages: • One sensor per Polygon • Node can calculate its VP by knowing only its immediate (Delaunay) neighbors • Smaller VP’s in high node density areas • Drawbacks • One sensor potentially in charge of large area • Paths likely to be close to border edges • How to find Delaunay neighbors?

29. Path Request • Path_request: Node sireceives a request from an agent to find PminE from I to D . • Using the grid based structure (Recall Centralized algo.), the node Si calculates the minimum exposure path from I to reach discrete points on the boundary edges. Si I

30. Edge Update • Each polygon edge has a corresponding Exposure Profile (EP) • Node s1 updates an EP e13 • s1 sends update message to neighbor node s3 • s3 computes new minimal exposure paths and updates all its EPs. • s3 sends appropriate EP update messages to corresponding neighbors

31. Abort Update • Edge update stops when • When EP at the search boundary is larger than the specified termination condition (parameter indicating bound on exposure) • Specified by the algorithm at first • Denoted by  • Guaranteed to converge since exposure is always increasing.

32. Dest Update • Parameter  is updated on reaching destination • set to minimum of exposure at destination point and the current value of  • This value is broadcasted throughout the network. • Terminate all search along paths having value greater than this updated value.

33. Simulation Results

34. Recent Work • Define Spatial fidelity • Parameter denoting the average number of nodes covering an area • Approach • Find number of nodes • covering a unit area • Multiply by appropriate weight • Weight characterizes the • confidence of the result

35. Recent work (contd.) • The effective node density from sensing perspective is • Probability that N nodes cover a point is given by

36. Some thoughts … • Fundamental question: Given an area A and the desired coverage • What is the minimum number of nodes required to achieve the desired coverage given the deployment scheme ? • What is the probability of achieving the desired coverage for a random deployment ? • Things to ponder about • What is the mapping from probability of detection to coverage ? • Sophisticated sensing model • Directional Sensing • Effect of obstacles • More than one type of sensors

37. Bibliography • Seapahn Meguerdichian, Farinaz Koushanfar, Miodrag Potkonjak, Mani Srivastava, "Coverage Problems in Wireless Ad-Hoc Sensor Networks." IEEE Infocom 2001, Vol 3, pp. 1380-1387, April 2001. • Seapahn Meguerdichian, Farinaz Koushanfar, Gang Qu, Miodrag Potkonjak, "Exposure In Wireless Ad Hoc Sensor Networks." Procs. of 7th Annual International Conference on Mobile Computing and Networking (MobiCom '01), pp. 139-150, July 2001. • Seapahn Meguerdichian, Sasa Slijepcevic, Vahag Karayan, Miodrag Potkonjak, "Localized Algorithms In Wireless Ad-Hoc Networks: Location Discovery and Sensor Exposure" MobiHOC 2001, pp. 106-116, October 2001. • Visit http://www.cs.ucla.edu/~seapahn/