1. Topological Hole Detection in Wireless Sensor Networks and its Applications Stefan Funke Department of Computer Science, Stanford University, U.S.A. DIAL-M-POMC 2005 Speaker ： Shih-Yun Hsu

2. DIAL-M-POMC  Discrete Algorithms and Methods for Mobile Computing and Communications  Workshop in conjunction with ACM/SIGMOBILE MobiCom (1997 ～ 2004)  Principles of Mobile Computing  Workshop in conjunction with  ACM/SIGACT and SIGOPS PODC (2001)  ACM/DISC (2002)

3. Outline  Introduction  Related works  Main methods  Topology hole finding  Coarse Boundary Sampling and Pruning  Applications  Experiment evaluation  Conclusions

4. Introduction  Due to cost restrictions and to achieve the maximum life-time by energy savings  The characteristics of sensors  Low-capability devices  Temperature  Humidity  Small radio device that allows for communication between nearby sensor nodes  Easy to be deployed by airplanes

5. Introduction  To achieve the maximum life-time  It is impossible to equip energy-hungry GPS unit  None of the sensor nodes is aware of its geographic location

6. Introduction  There are many holes in the monitoring region  Fall right into the flames and be destroyed  Plunge into a lake or pond and be unable to perform their monitoring task  Fall from airplane on the grand then break  Detecting the boundaries of such holes in the monitored space created by fire or other phenomena

7. Related works  GLIDER: Gradient Landmark-Based Distributed Routing for Sensor Networks  Geographic Routing without Location Information  MAP: Medial Axis Based Geometric Routing in Sensor Networks

8. Main methods  Topology hole finding  Coarse Boundary Sampling and Pruning

9. Topology hole finding  Basic concept Beacon Euclidean length hole Unit Disk Graph (UDG)

10. Topology hole finding  Monitoring (connected) region  Beacon  Any points  d p (x) denotes the minimum Euclidean length from p to x  The isolevel (contour of level) of k  The sub-graph of UDG induced by I(k) might be disconnected p x d p (x) I(k) C 1 (k) C 2 (k)

11. Topology hole finding  Pick a local beacon q  Compute hop-distances h(v’) to q  Mark all nodes v which do not have a 2-hop neighbor v’ with h(v’) > h(v) C 1 (k) q v

12. Topology hole finding beacon Border nodes

13. Topology hole finding

15.  The first beacon was chosen randomly  Maintain a variable CBD(v) (Closest Beacon Distance) storing the (hop-)distance and choose the last 3 beacons as far as possible 1 2 3 4

16. Coarse Boundary Sampling and Pruning  A natural way to reduce this number is to compute a maximal independent set (MIS) within all the marked nodes  Maximal independent sets in radio networks  Thomas Moscibroda, Roger Wattenhofer  Department of Computer Engineering and Networks Laboratory, ETH Zurich, Switzerland  ACM Symp. on PODC 2005

17. Coarse Boundary Sampling and Pruning

18. Density

19. Applications  GLIDER: Gradient Landmark-Based Distributed Routing for Sensor Networks  Qing Fang, Jie Gao, Leonidas J. Guibas, Vin de Silva, Li Zhang  Department of Electrical Engineering, Computer Science, Mathematics, Stanford University  Information Dynamics Lab, HP Labs  INFOCOM 2005

20. Applications -GLIDER- S D

21.  Paths that share the same subsequence of tiles are kept apart  Load-balance

22. Applications -GLIDER- GLIDER for random landmark selection GLIDER for topology-aware landmark selection

23. Applications -GLIDER-  In inter-tile, the GLIDER protocol is also load- balance

24. Applications -GLIDER-  In intra-tile, the GLIDER protocol could not be load-balance Near Far

25. Applications -GLIDER-  Load imbalance due to Landmarks being too close to boundaries

26. Applications -GLIDER-

27.  Landmarks sends a HELLO message with distance counter 0 which increases at every hop  The value △ (v) is then the minimum counter value over all messages received  d local (p)=min(d(p, q i ))  New position of landmark p’=d local (p)/3  p still in the tile of p’  Any tile will not contain a whole hole  If d(p’, q’)<d local (p) (p and q are closer)  Removed q’ p q1q1 q2q2 q3q3 q4q4 P’

28. Applications -GLIDER-

29. Applications  Geographic Routing without Location Information  Ananth Rao, Sylvia Ratnasamy, Christos Papadimitriou, Scott Shenker and Ion Stoica  University of California, Berkeley  INFOCOM 2003

30. Applications - Geographic Routing -

32.  Holes might obstruct the shortest paths between nodes of the network and hence their lengths are not a good estimate of the true geometric distance

33. Applications - Geographic Routing - Truthful distances Not truthful distances

34. Applications - Geographic Routing -  P is the set of boundary nodes  The distance measured between a pair is truthful, if the respective shortest path in the communication graph from p to q providing this estimate does not contain any as intermediate node

35. Applications - Geographic Routing -

36. Applications  MAP: Medial Axis Based Geometric Routing in Sensor Networks  Jehoshua Bruck, Jie Gao, Anxiao (Andrew) Jiang  California Institute of Technology, US  Caltech, US  MobiCom 2005

37. Applications -MAP-

43. Near Far to the border

44. Experiment evaluation  4900 nodes  800×800 square region  Communication range is 15(average degree 5), 20(10), 27(18), 40(39)  The degree is r communication /r sense  Unit disk graphs (UDG)  Random Uniform Distributions  Randomly perturbed Grid  Non-UDG

45. UDG with Random Uniform Distributions 15(5) 20(10) 27(18) 40(39) Communication Range (Ave. degree)

46. UDG with Randomly perturbed Grid 15(5) 20(10) 27(18) 40(39) Communication Range (Ave. degree)

47. Non-UDG With UDG With Non-UDG

48. Non-UDG Degree 8Degree 16 Degree 20

49. Conclusions  This paper we have presented a rather simple and straightforward algorithm for detecting holes in a wireless communication network  Location-unaware  Higher density is better  This paper also sketched further applications of hole finding routine, where the knowledge about holes in the network provides for better performance of existing topology-based, location-free protocols

50. Thank You!!