1. Locating and Bypassing Routing Holes in Sensor Networks Authors: Qing Fang, Jie Gao and Leonidas J. Guibas Presented by: Yinfei Pan

2. Introduction Sensor networks –Usually vast in their scale –Lost cost per node –mostly static –Energy is an very important consideration routing cannot be too heavy –AODV, DSR, and Flooding may have more cost –Need new routing mechanism design Geographical Routing may be a good choice

3. GPSR Location of the destination node is assumed to be known Each node knows location of its neighbors Each node forwards a packet to its neighbor closest to the destination (greedy forwarding) If routing holes are found, uses perimeter routing

4. GPSR Perimeter routing requires the maintenance of the underlying planar graph (too expensive in sensor networks) In fact, perimeter routing are not used most of the time –Karp and Kung’s results show that most forwarding is through greedy forwarding –So, keeping a planar graph at every node all the time, which is used only occasionally seems unnecessary.

5. The Purpose of This Paper Situation: packet stuck at a node all of whose 1 hop neighbors are further away from the destination (Local minimum) Find underlying geometric properties behind the local minimum phenomenon. –Seemingly unorganized structures have structures –Explore holes in sensor networks A closed cycle with no self intersections bounding a closed region

6. Why Holes Important Geographic multi-cast: routing to a geographic region Detection of the boundary of disaster regions Geographic properties of the underlying terrain Detecting regions with low sensor density due to depletion of node power. Information storage mechanisms

7. What’s Done by This Paper Incorporate stuck nodes into routing research Local TENT rule to determine whether a node is a stuck node Find holes: BOUNDHOLE (a distributed algorithm)

8. First Method to Identify Holes Definitions –Weak stuck node P P is the closest node to node Q (among P’s neighbors), and Q is out of the communication range of P (Assume each has radius 1) Q is called black node P J H Q

10. Holes Finding S is a set of nodes Vornoi Diagram partitions plane into Vornoi cells (All points within a cell are closest to only one node) Delaunay triangulation: connecting nodes that are in adjacent cells (dual graph of Vornoi) Delaunay triangle has “emptycircle” property –circumcircle contains no nodes of S inside

11. Holes Finding In the Delaunay triangulation if all the edges adjacent to a node p are not longer than 1, then P is not a stuck node (within communication range) Possible stuck nodes: nodes with at least one adjacent delaunay edges longer than 1.

12. Holes Finding Restricted Delaunay Graph (RDG): A sub graph of DT with only edges <=1 are kept. A hole is a face in the RDG with at least 4 vertices.

13. Drawback of The First Method The algorithm for computing the Delaunay triangulation is a centralized algorithm –a heavy algorithm for sensor networks the set of nodes identified using this method, is a super set of the set of real weak stuck nodes. the destination may not be a node in the network, –You just want you data multicast to a specific region

15. Improved Method to Identify Holes Strong Stuck nodes –Node p if there exists a location q outside p’s transmission range so that no neighbor of p is closer to q than itself. –Collection of Qs is called black region –So this strong definition is in fact to extend one black point to a black region (Includes weak def.) P J H Black Region Q

17. TENT Rule For each p, order all of its neighbors counterclockwise For each adjacent pair (u, v) draw perpendicular bisector of the two edges with p (u, p) (v p) These intersect at a center O. If O is in communication range of p, then no black region (all in communication range) We say p cannot be stuck in the direction upv

18. TENT Rule Define a stuck angle at a node p is the angle spanned by a pair of adjacent neighbors of node p in which the direction of p becomes the local minimum (no neighbor in this area was found to be more closer to the destination) A node is strong stuck if it has at least one stuck angle If angle upv is <120 degrees, p cannot be stuck (just the point black region disappear) a node can have at most 3 stuck directions The computation of TENT Rule can be preformed with only information on 1-hop neighbors.

19. Possible Stuck Node v

20. Holes Finding BOUNDHOLE –Simply greedy sweeping algorithm –Hole is a closed region bounded by a non self intersecting polygonal loop –A hole H belongs to a strong stuck node v if H is identical to the loop formed by BOUNDHOLE starting at v –u is an upstream node of v if u is the previous hop neighbor sharing same boundary of a Hole with v in a clockwise order –When finding a hole’s boundary, the right-hand side of the edge is inside the hole

21. BOUNDHOLE Assume P is a stuck node, stuck direction is spt1 Step 1. use the right hand rule starting at t1. Take the t2 by sweeping from p counterclockwise. Step 2. Continued until pt1t2 … tk goes back to p Step 3: Solve Edge Intersection (next slide)

22. BOUNDHOLE tj tj+1 intersects ti ti+1 There are two cases –tj not visible to ti and ti+1, Delete ti+1… tj+1 and continue Form a new sequence of t0t1 · · · (ti)(tj+1)(tj)

23. BOUNDHOLE Intersects solving (cont.) –ti not visible to tj and tj+1, take ti+1 as the next hop for tj Form a new sequence of t0 · · · (tj)(ti+1)(ti)

24. BOUNDHOLE Can Work For each three consecutive nodes in the sequence, the third one is not visible to the first one. Each node one the boundary of hole appear at most 6 times (prove see paper since too complex) So, in generating the sequence, we are indeed making progresses, and when travel through the boundary, we are in an finite set.

25. BOUNDHOLE is Distributed One stuck direction is simple and localized. The computation at each node depends only on the 1-hop neighbors. Thus the algorithm is distributed Thus, this method scales well to large networks

26. Result (Tighter than Delaunay Triangulation)

27. Optimizations Suppressed Start –The Hole finding stages Initially gather 1-hop info Then run TENT to determine if it is a stuck node BOUNDHOLE begin to find boundary of hole –Stuck nodes initiate messenger packet in direction of being stuck. Consider the graph in next slide

28. Suppressed Start All stuck nodes compute same hole (see left) Duplication causes unnecessary traffic So, assign each init package an ID, then drop redundant packets –When package comes from ingress edge that an earlier messenger packet with a lower ID has taken, drop it.

29. Wrong Case See right, consider two loop: j – l – n – o – p – i - j and loop k – m – n – o – p – i – j – k We have problem! k try to identify its hole, but its package will be dropped by o, p, or I How to fix: Set an Enforce Bit to not drop –Is this method actually solve the problem??

30. Node failures Failures can create new holes and change boundaries of existing holes periodically broadcast to its neighbors, if no response for 3 times, then do BOUNDHOLE NOTICE: To deal with Node failures, the enforce bit must be set this time However, won’t this cause more communication cost for only one node change –My suggestion: Use enforce state, not just a bit, when BOUNDHOLE in this case met the common edge stop the hole finding process and we still could get a hole correct whole loop

31. Routing Stages Greedy forwarding as GPSR Get stuck: route the packet along the boundary of the hole. When gets to a node more closer to destination, back to Greedy forwarding If inside the hole but not reachable after tour around the boundary, do "flooding“ –Can compute the better side by storing shape of the hole

32. Conclusion Information saving and computing is only on problematic parts of the network –only node on the body of a hole need to store additional information upstream and downstream neighbors boundary sharing he shape of the boundary (optional) Result: energy saving, low memory demand, fast response

33. Contribution Initiate research on studying the structures of sensor networks Provide an effective method to explore such structure Problems & Improvement see the following slides …

34. Problems & Improvement Suggestions on this paper Lack simulation results - only some topology graphs are available To find hole, it is necessary for the use of suppressed start, but as the paper itself shows, this is problematic and enforce bit seems do not solve the problem at all (When to set that bit in general case?) The underlying assumption of this paper, which we can say the fundamental issue of this paper is the communication range is an ideal circle which is not true in real world, so, this need to be improved Improvement suggestion see next slide …

35. Problems & Improvement Suggestions on this paper One stuck node own a hole, and there are many nodes on the boundary, is the hole be found actually like the physical structure? Highly untenable. Improvement Suggestion: In fact, this paper based on an ideal circle as the communication range, so the TENT Rule in fact is just to rule out all the possibility inside the communication range of a node since those nodes must not be in a void area which identified in this paper as a hole. For most of the other nodes which do not comply the TENT Rule, this paper in fact assumes them as in void region, so it get a super set of actual holes. In real world, communication range definitely is NOT that ideal and link quality is also a very important issue, the basic ideal of TENT Rule is still great valuable, but we can improve it, and make it more complex by incorporation the real geometrical shape of communication range.