Area Coverage

1. Area Coverage Sensor Deployment and Target Localization in Distributed Sensor Networks

2. Area Coverage

3. Area Coverage • Objective • Maximize the coverage for a given number of sensors within a wireless sensor networks. • Propose a Virtual force algorithm (VFA)

4. Area Coverage • Virtual Force Algorithm(VFA) • Attractive force • Repulsive force

5. Area Coverage • Virtual Force Algorithm(VFA) • Each sensor behaves as a “source of force” for all other sensors S2 • Attractive force S3 → → → S1 F13 F12 F14=0 • Repulsive force S4

6. Area Coverage • Virtual Force Algorithm(VFA) • Fij: the vector exerted on Siby another sensor Sj • Obstacles and areas of preferential coverage also have forces acting on Si • FiA : the total (attractive) force on Si due to preferential coverage areas • FiR : the total (repulsive) force on Si due to obstacles • The total force Fion Si → → → →

7. Area Coverage • Virtual Force Algorithm(VFA) • Uses a force-directed approach to improve the coverage after initial random deployment • Advantages • Negligible computation time • Flexibility

8. Area Coverage Movement-Assisted Sensor Deployment

9. Area Coverage • Motivation sensor sensing range

10. Area Coverage • Deploying more static sensors cannot solve the problem due to wind or obstacles

11. Area Coverage • General idea:

12. sensing range Area Coverage • Coverage Hole Detection Only check local Voronoi cell

13. Area Coverage

14. C C A A B B Area Coverage • The VECtor-Based Algorithm (VEC) • Motivated by the attributes of electrical particles • Virtual force pushes sensors away from dense area

15. M M B Area Coverage • The VORonoi-Based Algorithm (VOR) • Move towards the farthest Voronoi vertex • Avoid moving oscillation: stop for one round if move backwards B

16. B B M M N N Area Coverage • The Minimax Algorithm • Move to where the distance to the farthest voronoi vertex is minimized

17. Target Coverage Energy-Efficient Target Coverage in Wireless Sensor Networks

18. Target Coverage Sleep • Area coverage problem • Sensing overall area • Minimizing active nodes • Maximizing network lifetime Active

19. Target Coverage Sleep Target • Target coverage problem • Sensing all targets • Minimizing active nodes • Maximizing network lifetime Active

20. Target Coverage • Disjoint Set Covers • Divide sensor nodes into disjoint sets • Each set completely monitor all targets • One set is active each time until run out of energy • Goal: To find the maximum number of disjoint sets • This is NP-Complete

21. Target Coverage s1 r1 s2 All sensors are active Lifetime = 1 r2 s3 r3 s4 s1 r1 s3 r2 Sensor Target s4 r3 s2

22. Target Coverage s1 r1 s2 Disjoint sets S1 = {s1, s2} S2 = {s3, s4} Lifetime = 2 r2 s3 r3 s4 s1 r1 s3 r2 Sensor Target s4 r3 s2

23. Target Coverage s1 t4 t1 t2 t3 r1 s2 Another Approach: S1 = {s1, s2} with t1 = 0.5 S2 = {s2, s3} with t2 = 0.5 S3 = {s1, s3} with t3 = 0.5 S4 = {s4} with t4 = 1 Lifetime = 2.5 r2 s3 r3 s4 s1 r1 s3 r2 s4 r3 s2

24. Target Coverage s1 r1 s2 r2 s3 r3 s4 s1 r1 s3 r2 s4 r3 s2

25. Target Coverage • Set active interval = 0.5 • choose a available set S1 S2 S3 S4 S4 • This order is not unique, tried all the orders and pick up the order with the maximum life time

26. Target Coverage • Maximum Set Covers (MSC) Problem • Given: • C : set of sensors • R : set of targets • Goal: • Determine a number of set covers S1, …, Sp and t1,…, tp • where: • Si completely covers R • Maximize t1 + … + tp • Each sensor is not active more than 1 • MSC is NP-Complete

27. Target Coverage s1 r1 • Using Linear Programming Approach • Given: • A set of n sensor nodes: C = {s1, s2, …, sn} • A set of m targets: R={r1, r2, …, rm} • The relationship between sensors and targets: Ck = {i|sensorsi covers target rk} C = {s1, s2, s3}; R = {r1, r2, r3} C1 = {1, 3}; C2 = {1, 2}; C3 = {2, 3} • Variables: • xij = 1 if si ∈ Sj, otherwise xij = 0 • tj ∈[0, 1], represents the time allocated for Sj s2 r2 s3 r3

28. Target Coverage maximize network lifetime sensor’s lifetime constraint all targets must be covered 28

29. Barrier Coverage Strong Barrier Coverage of Wireless Sensor Networks

30. Barrier Coverage USA MEXICO

31. Barrier Coverage • How to define a belt region? • Parallel curves • Region between two parallel curves

32. Barrier Coverage • Two special belt region • Rectangular: • Donut-shaped:

33. Barrier Coverage • Crossing paths • A crossing path is a path that crosses the complete width of the belt region. Crossing paths Not crossing paths

34. Barrier Coverage Weak barrier coverage Strong barrier coverage

35. Barrier Coverage • k-covered • A crossing path is said to be k-covered if it intersects the sensing disks of at least k sensors. 3-covered 1-covered 0-covered

36. Barrier Coverage • k-barrier covered • A belt region is k-barrier covered if all crossing paths are k-covered. Not barrier coverage 1-barrier coverage

37. Barrier Coverage • Reduced to k-connectivity problem • Given a sensor network over a belt region • Construct acoverage graph G(V, E) • V: sensor nodes, plus two dummy nodes L, R • E: edge (u,v) if their sensing disks overlap • Region is k-barrier covered if L and R are k-connected in G. R L

38. Barrier Coverage 3-barrier 3-barrier

39. Barrier Coverage • Characteristics • Improved robustness of the barrier coverage • Lower communication overhead and computation costs • Strengthened local barrier coverage failure failure with vertical strip without vertical strip 42

40. Surface Coverage in Wireless Sensor NetworksIEEE INFOCOM 2009 Ming-Chen Zhao, Jiayin Lei, Min-You Wu, Yunhuai Liu, Wei ShuShanghai Jiao Tong Univ., Shanghai

41. Motivation • Existing studies on Wireless Sensor Networks (WSNs) focus on 2D ideal plane coverage and 3D full space coverage. • The 3D surface of a targeted Field of Interest is complex in many real world applications. • Existing studies on coverage do not produce practical results.

42. Motivation • In surface coverage, the targeted Field of Interest is a complex surface in 3D space and sensors can be deployed only on the surface. • Existing 2D plane coverage is merely a special case of surface coverage. • Simulations point out that existing sensor deployment schemes for a 2D plane cannot be directly applied to surface coverage cases.

43. Introduction • volcano monitoring

44. Introduction • Surface Coverage • use triangularization to partition a surface

45. Models • Sensor models • sensing radius r in 3D Euclid space • statically deployed • Surface models • z = f(x,y) • z = c, if the surface is a plane ax + by + c, if the surface is a slant

46. Problem Statement • Problems in WSN surface coverage: • 1. Thenumber of sensors that are needed to reach a certain expected coverage ratio under stochastic deployment.

47. Problem Statement • Problems in WSN surface coverage: • 2. The optimal deployment strategy with guaranteed full coverage and the least number of sensors when sensor deployment is pre-determined.

48. Optimum Partition Coverage Problem (OPCP) • Convert optimum surface coverage problem to a discrete problem and then relate those results back to the original continuous problem.

49. Optimum Partition Coverage Problem (OPCP) • S: P = {SA, SB, SC, SD, SE, SF} h*(Lα)=h(1)∪h(3)∪h(4)∪h(5) Lα = {1, 3, 4, 5} |Lα| = 4 Lβ = {3, 6, 7} |Lβ| = 3minimum 1 6 A B 2 F C 7 E 5 3 D 4

50. Optimum Partition Coverage Problem (OPCP) • Algorithm 1: Greedy algorithm 1 6 A B 2 F C 7 E 5 3 D 4