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					GPSR: Greedy Perimeter Stateless
Routing for Wireless Networks

 B. Karp, H. T. Kung

 Borrowed some slides from Richard Yang’s




                                            1
Motivation
 A sensor net consists of hundreds or thousands of
  nodes
      Scalability is the issue
      Existing ad hoc net protocols, e.g., DSR, AODV, ZRP,
       require nodes to cache e2e route information
      Dynamic topology changes
      Mobility
 Reduce caching overhead
    Hierarchical routing is usually based on well defined, rarely
     changing administrative boundaries
    Geographic routing
        • Use location for routing


                                                                     2
Scalability metrics
 Routing protocol msg cost
      How many control packets sent?
 Per node state
    How much storage per node is required?

 E2E packet delivery success rate




                                              3
Assumptions
 Every node knows its location
   Positioning devices like GPS
   Localization

 A source can get the location of the
  destination
 802.11 MAC
 Link bidirectionality



                                         4
Geographic Routing: Greedy Routing



                                 Closest
                                  to D

        S                                                 D
                         A

- Find neighbors who are the closer to the destination
- Forward the packet to the neighbor closest to the destination

                                                                  5
Benefits of GF

 A node only needs to remember the location
  info of one-hop neighbors
 Routing decisions can be dynamically made




                                               6
Greedy Forwarding does NOT always work


                                GF fails




 If the network is dense enough that each
  interior node has a neighbor in every 2/3
  angular sector, GF will always succeed
                                               7
Dealing with Void: Right-Hand Rule




  Apply the right-hand rule to traverse the
   edges of a void
    Pickthe next anticlockwise edge
    Traditionally used to get out of a maze
                                               8
Right Hand Rule on Convex Subdivision




For convex subdivision, right hand rule is equivalent to
traversing the face with the crossing edges removed.


                                                           9
Right-Hand Rule Does Not Work with
Cross Edges



           z
     u
                          D



                         x originates a packet to u
 w
                       Right-hand rule results in the
                      tour x-u-z-w-u-x
               x

                                                         10
Remove Crossing Edge


         z
     u
                     D



                 Make   the graph planar
 w
                 Remove   (w,z) from the graph
             x    Right-hand rule results in the
                 tour x-u-z-v-x
                                                    11
Make a Graph Planar
 Convert a connectivity graph to planar non-
   crossing graph by removing “bad” edges
     Ensure the original graph will not be
      disconnected
     Two types of planar graphs:
      •   Relative Neighborhood Graph (RNG)
      •   Gabriel Graph (GG)




                                                12
Relative Neighborhood Graph
 Connection  uv can exist if
  w  u, v, d(u,v) < max[d(u,w),d(v,w)]   not empty 
                                           remove uv




                                                         13
Gabriel Graph
 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, d2(u,v) < [d2(u,w) + d2(v,w)]
                                                   Not empty 
                                                   remove uv




                                                                       14
Properties of GG and RNG
                                 RNG
 RNG is a sub-graph of
  GG
     Because RNG removes more
      edges
                                 GG

 If the original graph is
  connected, RNG is also
  connected



                                       15
Connectedness of RNG Graph
 Key observation
   Any edge on the minimum
    spanning tree of the original
    graph is not removed
   Proof by contradiction: Assume
    (u,v) is such an edge but removed in RNG

                        w



                u           v

                                               16
 Examples




   Full graph               GG subset             RNG subset

• 200 nodes
• randomly placed on a 2000 x 2000 meter region
• radio range of 250 m

•Bonus: remove redundant, competing path  less collision      17
Greedy Perimeter Stateless Routing (GPSR)
 Maintenance
      all nodes maintain a single-hop neighbor table
      Use RNG or GG to make the graph planar

 At source:
      mode = greedy

 Intermediate node:
      if (mode == greedy) {
         greedy forwarding;
         if (fail) mode = perimeter;
       }
       if (mode == perimeter) {
         if (have left local maxima) mode = greedy;
         else (right-hand rule);
       }
                                                        18
GPSR



                         greedy fails



 Greedy Forwarding                            Perimeter Forwarding




                     have left local maxima
   greedy works                                   greedy fails


                                                                     19
Implementation Issues
 Graph planarization
   RNG & GG planarization depend on having the
    current location info of a node’s neighbors
   Mobility may cause problems
   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
    Also, assumes a circular radio transmission model
    In general, it could be harder & more expensive
     than it sounds

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



                                                         21
 50, 112 & 200 nodes
   22 sending nodes & 30 flows
   About 20 neighbors for each node – very dense
   CBR (2Kbps)

 Nominal radio range: 250m (802.11 WaveLan
  radio)
 Each simulation takes 900 seconds
 Take an average of the six different
  randomly generated motion patterns

                                                    22
Packet Delivery Success Rate




                               23
Routing Protocol Overhead




                            24
Related Work
 Geographic and Energy Aware Routing
  (GEAR), UCLA Tech Report, 2000
     Consider remaining energy in addition to
      geographic location to avoid quickly draining
      energy of the node closest to the destination
 Geographic probabilistic routing,
  International workshop on wireless ad-hoc
  networks, 2005
     Determine the packet forwarding probability to
      each neighbor based on its location, residual
      energy, and link reliability
                                                       25
 Beacon vector routing, NSDI 2005
    Beacons know their locations
    Forward a packet towards the beacon

 A Scalable Location Service for Geographic Ad Hoc
  Routing, MobiCom ’00
      Distributed location service
 Landmark routing
    Paul F. Tsuchiya. Landmark routing: Architecture,
     algorithms and issues. Technical Report MTR-87W00174,
     MITRE Corporation, September 1987.
    Classic work with many follow-ups




                                                             26
Questions?




             27

				
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