1 Distributed Navigation Algorithms for Sensor Networks Chiranjeeb Buragohain, Divyakant Agrawal, Subhash Suri Dept. of Computer Science, University of California, Santa Barbara, CA 93106, USA IEEE INFOCOM 2006

2 Outlines Main ideas Previous works Navigation using uniform skeleton graph Navigation using adaptive skeleton graph Experimental Results Conclusions

3 Main ideas Distributed algorithms to aid navigation of a user through area covered by sensors. Danger zone, danger point, safe path Flooding (optimal) vs. reduced graph (approximately optimal ) Basic solution Construct a reduced graph Carry out a search on the skeleton graph to find shortest path/minimal exposure paths over the skeleton graph only

4 Previous works GPSR (Greedy Perimeter Stateless Routing) Local search Low communication cost, but low performance Stateless is not meant literally, but refers to this small, purely local state. Flooding Global search High performance, but high communication cost [9] B. Karp and H. T. Kung, “GPSR: greedy perimeter stateless routing for wireless networks,” in Proc. of MOBICOM 2000.

5 References [8] Q. Li, M. DeRosa, and D. Rus, “Distributed algorithms for guiding navigation across a sensor network,” in Proc. of IPSN ’03., [9] B. Karp and H. T. Kung, “GPSR: greedy perimeter stateless routing for wireless networks,” in Proc. of MOBICOM [14] S. Meguerdichian, F. Koushanfar, G. Qu, and M. Potkonjak, “Exposure in wireless ad-hoc sensor networks,” in Proc. of MOBICOM 2001, [15] G. Veltri, Q. Huang, G. Qu, and M. Potkonjak, “Minimal and maximal exposure path algorithms for wireless embedded sensor networks,” in Proc. of SenSys 2003, 2003.

6 Danger Zone Shortest feasible path Danger Point Minimum exposure path Probability of detection where R is the Euclidean distance from the point of danger to the point (x, y) The potential function φ(x, y) itself is arbitrary, but it should monotonically decrease as we move away from the enemy position.

7 The superposition property ：

8 x cx

9

10 Shortest Path Algorithm BFS When BFS terminates, every node knows its distance to the source and its parent point points to its parent along the path toward the source. Every packet contains two fields How many hop it has traveled from the source The last node visited Every node maintains a distance variable If a node receives multiple search packets from source, only packets with smallest hop counts are forwarded. Proposition : In a network of n nodes, the number of total packet transmissions required for the shortest path algorithm is O(n).

11 Minimum Exposure Path Algorithm When the algorithm terminates, every node knows the exposure of the minimum exposure path to the source.

12 Greedy Perimeter Stateless Routing for Wireless Networks (GPSR) It is a greedy routing strategy for ad hoc networks which utilizes geographic information to find its destination.

13 Alternatives protocol : DSR, AODV DSR : Dynamic Source Routing AODV : Ad-Hoc On-Demand Distance Vector Routing Do not utilize geographic information and instead flood the network with query packets for finding routes.

14 Perimeter routing - 1 Two paths : (x  y  z  D) and (x  w  v  D)

15 Perimeter routing - 2 Traversing the cycle (x  w  v  D  z  y  x) by the right-hand rule amounts to navigating around the pictured void.

16 Outlines Main ideas Previous works Navigation using uniform skeleton graph Navigation using adaptive skeleton graph Experimental Results

17 Navigation Using Uniform Skeleton Graph (USG) Step 1: Construct a reduced graph Ex: GPSR Step 2: Carry out a search on the skeleton graph to find shortest paths and minimal exposure paths

18 Construct a reduced graph Some node initiates the grid street construction protocol. Using GPSR. Next we turn to the embedding of the perimeter street. Detect the danger zone boundary The node inside the danger zone can go to sleep The boundary node broadcast “wake up” message with life time of w hop to its neighbor.

19 grid streets : The grid streets are a square grid of lines separated by distance s from each other. Perimeter streets : An additional set of streets which follow the perimeter of the danger zone is also included in the street map and they are the perimeter streets.

21

22 Load balancing by shifting How to avoid running out energy This can be avoided by varying the value of s, the street separation; or by shifting all the streets by a constant amount in the diagonal direction.

23 How to discover a path that points not on streets ? What can one do for source and destination pairs which do not lie on any street? If the destination does not lie on any street, then it is enclosed in a square enclosed by four streets. Methods The destination can be found by flooding that limited square. Construct the streets on-demand. Automatic load balancing

24 Navigation Using Uniform Skeleton Graph (USG) Step 1: Construct a reduced graph Ex: GPSR Step 2: Carry out a search on the skeleton graph to find shortest paths and minimal exposure paths

25 The USG: basic properties

26 ＆ b a L

27 2D 3D L L cD

28

29 Outlines Main ideas Previous works Navigation using uniform skeleton graph Navigation using adaptive skeleton graph Experimental Results

30 Navigation Using Adaptive Skeleton Graph (ASG) Idea of ASG Place streets densely near danger zones while sparsely far away from danger zones How do they achieve that? Recursively divide the area into quadtree 四分樹 until no quadtree cell whose boundary is intersected by danger zones boundary.

31

32 Illustration of Constructing street map for ASG (Shortest Path)

33 Illustration of Constructing street map for ASG (Minimum Exposure Path) The sensor at a danger point flood with BFS Every node finds it is equidistant from any two point declared as Voronoi edge Embeding street map on Voronoi edge using quadtree as before The danger point : A,B,C

34 Performance of ASG ASG improves (compared to USG) not only the number of nodes Implies lower communication cost but also the total path length Implies performance boosting

35 Theorem 4 : ASG basic property – 1 (minimum communication cost) Communication cost of discovering the shortest path is The limits of communication cost is the limits of the size (length) of ASG So we prove that the size of ASG is

36 # of node cross Perimeter Length of the node Total length of street at that level By definition of well-behaved curve : Total length of street at all levels Communication cost of ASG:

37 Theorem 5 : ASG basic property -2 (shortest path) For a path joining any two points located on the streets in the adaptive skeleton graph l ASG l OPT x worst case x/2 x

38 Theorem 6 : ASG basic property – 3 (minimum exposure path) For a path joint any two points located on the street in ASG The proof is the same as corresponding Theorem for USG (Theorem 3), the size of square did not used in that proof, so SASG : the exposure for the adaptive skeleton graph.

39 Performance Comparison USG with ASG USGASG Communication Cost Performance Radio of Shortest Path Performance Radio of Minimum Exposure Path

40 Outlines Main ideas Previous works Navigation using uniform skeleton graph Navigation using adaptive skeleton graph Experimental Results

41 Experimental Results Place n sensors in a area Do the experiment with n =1024, 4096 and nodes. Shortest path is tested with two types of danger zones

42 Experimental Results (Skeleton Graph Size v.s. Number of Nodes) 337 nodes ~37% 659 nodes ~4% S : Simple C : Complex The uniform skeleton graph is slightly larger than the adaptive graph, but this difference is not highly significant.

43 Experimental Results (Performance ratio for Shortest Path) Performance Ratio = Generate 200 random point pairs lying within the sensor coverage area The approximated path lengths are no worse than 50% of optimal, The adaptive skeleton graph performs better as expected.

44 Experimental Results (Performance ratio for Minimum Exposure Path) Use 20 different scenarios, each of which consists of three danger points Compute 10 minimum exposure paths Performance Ratio = Both the uniform and adaptive skeleton graphs perform equally well with neither holding a decisive advantage.

45 Conclusions Shortest path and minimum exposure path can be solved using skeleton graph The USG and ASG provide close to optimal paths with very low communication overhead ASG is more scalable than USG

46 References [8] Q. Li, M. DeRosa, and D. Rus, “Distributed algorithms for guiding navigation across a sensor network,” in Proc. of IPSN ’03., [9] B. Karp and H. T. Kung, “GPSR: greedy perimeter stateless routing for wireless networks,” in Proc. of MOBICOM [14] S. Meguerdichian, F. Koushanfar, G. Qu, and M. Potkonjak, “Exposure in wireless ad-hoc sensor networks,” in Proc. of MOBICOM 2001, [15] G. Veltri, Q. Huang, G. Qu, and M. Potkonjak, “Minimal and maximal exposure path algorithms for wireless embedded sensor networks,” in Proc. of SenSys 2003, 2003.