1. 1 GPSR: Greedy Perimeter Stateless Routing for Wireless Networks B. Karp, H. T. Kung Borrowed slides from Richard Yang

2. 2 Motivation r A sensor net consists of hundreds or thousands of nodes m Scalability is the issue m Existing ad hoc net protocols, e.g., DSR, AODV, ZRP, require nodes to cache e2e route information m Dynamic topology changes m Mobility r Reduce caching overhead m Hierarchical routing is usually based on well defined, rarely changing administrative boundaries m Geographic routing Use location for routing

3. 3 Scalability metrics r Routing protocol msg cost m How many control packets sent? r Per node state m How much storage per node is required? r E2E packet delivery success rate

4. 4 Assumptions r Every node knows its location m Positioning devices like GPS m Localization r A source can get the location of the destination r 802.11 MAC r Link bidirectionality

5. 5 Geographic Routing: Greedy Routing S D Closest to D A - Find neighbors who are the closer to the destination - Forward the packet to the neighbor closest to the destination

6. 6 Benefits of GF r A node only needs to remember the location info of one-hop neighbors r Routing decisions can be dynamically made

7. 7 Greedy Forwarding does NOT always work r If the network is dense enough that each interior node has a neighbor in every 2  /3 angular sector, GF will always succeed GF fails

8. 8 Dealing with Void: Right-Hand Rule r Apply the right-hand rule to traverse the edges of a void m Pick the next anticlockwise edge m Traditionally used to get out of a maze

9. 9 Right Hand Rule on Convex Subdivision For convex subdivision, right hand rule is equivalent to traversing the face with the crossing edges removed.

10. 10 Right-Hand Rule Does Not Work with Cross Edges u z w D x x originates a packet to u Right-hand rule results in the tour x-u-z-w-u-x

11. 11 Remove Crossing Edge u z w D x Make the graph planar Remove (w,z) from the graph Right-hand rule results in the tour x-u-z-v-x

12. 12 Make a Graph Planar  Convert a connectivity graph to planar non- crossing graph by removing “bad” edges m Ensure the original graph will not be disconnected m Two types of planar graphs: Relative Neighborhood Graph (RNG) Gabriel Graph (GG)

13. 13 Relative Neighborhood Graph r Connection uv can exist if  w  u, v, d(u,v) < max[d(u,w),d(v,w)] not empty  remove uv

14. 14 Gabriel Graph r An edge (u,v) exists between vertices u and v if no other vertex w is present within the circle whose diameter is uv.  w  u, v, d 2 (u,v) < [d 2 (u,w) + d 2 (v,w)] Not empty  remove uv

15. 15 Properties of GG and RNG r RNG is a sub-graph of GG m Because RNG removes more edges r If the original graph is connected, RNG is also connected RNG GG

16. 16 Connectedness of RNG Graph r Key observation m Any edge on the minimum spanning tree of the original graph is not removed m Proof by contradiction: Assume (u,v) is such an edge but removed in RNG u v w

17. 17 200 nodes randomly placed on a 2000 x 2000 meter region radio range of 250 m Bonus: remove redundant, competing path  less collision Full graphGG subsetRNG subset Examples

18. 18 Greedy Perimeter Stateless Routing (GPSR) r Maintenance m all nodes maintain a single-hop neighbor table m Use RNG or GG to make the graph planar r At source: m mode = greedy r Intermediate node: m if (mode == greedy) { greedy forwarding; if (fail) mode = perimeter; } if (mode == perimeter) { if (have left local maxima) mode = greedy; else (right-hand rule); }

19. 19 GPSR Greedy ForwardingPerimeter Forwarding greedy fails have left local maxima greedy works greedy fails

20. 20 Implementation Issues r Graph planarization m RNG & GG planarization depend on having the current location info of a node’s neighbors m Mobility may cause problems m Re-planarize when a node enters or leaves the radio range What if a node only moves in the radio range? To avoid this problem, the graph should be re-planarize for every beacon msg m Also, assumes a circular radio transmission model m In general, it could be harder & more expensive than it sounds

21. 21 Performance evaluation r Simulation in ns-2 r Baseline: DSR (Dynamic Source Routing r Random waypoint model m A node chooses a destination uniformly at random m Choose velocity uniformly at random in the configurable range – simulated max velocity 20m/s m A node pauses after arriving at a waypoint – 300, 600 & 900 pause times

22. 22 r 50, 112 & 200 nodes m 22 sending nodes & 30 flows m About 20 neighbors for each node – very dense m CBR (2Kbps) r Nominal radio range: 250m (802.11 WaveLan radio) r Each simulation takes 900 seconds r Take an average of the six different randomly generated motion patterns

23. 23 Packet Delivery Success Rate

24. 24 Routing Protocol Overhead

25. 25 Related Work r Geographic and Energy Aware Routing (GEAR), UCLA Tech Report, 2000 m Consider remaining energy in addition to geographic location to avoid quickly draining energy of the node closest to the destination r Geographic probabilistic routing, International workshop on wireless ad-hoc networks, 2005 m Determine the packet forwarding probability to each neighbor based on its location, residual energy, and link reliability

26. 26 r Beacon vector routing, NSDI 2005 m Beacons know their locations m Forward a packet towards the beacon r A Scalable Location Service for Geographic Ad Hoc Routing, MobiCom ’00 m Distributed location service r Landmark routing m Paul F. Tsuchiya. Landmark routing: Architecture, algorithms and issues. Technical Report MTR-87W00174, MITRE Corporation, September 1987. m Classic work with many follow-ups

27. 27 Questions?