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GPSR: Greedy Perimeter Stateless Routing for Wireless Networks. B. Karp, H. T. Kung Borrowed some slides from Richard Yang’s. Motivation. A sensor net consists of hundreds or thousands of nodes Scalability is the issue

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GPSR: Greedy Perimeter Stateless Routing for Wireless Networks

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GPSR: Greedy Perimeter Stateless Routing for Wireless Networks

B. Karp, H. T. KungBorrowed some slides from Richard Yang’s


  • 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

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


  • Every node knows its location

    • Positioning devices like GPS

    • Localization

  • A source can get the location of the destination

  • 802.11 MAC

  • Link bidirectionality

Closest to D


Geographic Routing: Greedy Routing



  • Find neighbors who are the closer to the destination

  • Forward the packet to the neighbor closest to the destination

Benefits of GF

  • A node only needs to remember the location info of one-hop neighbors

  • Routing decisions can be dynamically made

Greedy Forwarding does NOT always work

  • 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

Dealing with Void: Right-Hand Rule

  • Apply the right-hand rule to traverse the edges of a void

    • Pick the next anticlockwise edge

    • Traditionally used to get out of a maze

Right Hand Rule on Convex Subdivision

For convex subdivision, right hand rule is equivalent to

traversing the face with the crossing edges removed.

Right-Hand Rule Does Not Work with Cross Edges




  • x originates a packet to u

  • Right-hand rule results in the tour x-u-z-w-u-x



Remove Crossing Edge




  • Make the graph planar

  • Remove(w,z)from the graph

  • Right-hand rule results in the tour x-u-z-v-x



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)

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

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

Properties of GG and RNG


  • RNG is a sub-graph of GG

    • Because RNG removes more edges

  • If the original graph isconnected, RNG is also connected



Connectedness of RNG Graph

  • Key observation

    • Any edge on the minimumspanning tree of the originalgraph is not removed

    • Proof by contradiction: Assume (u,v) is such an edge but removed in RNG




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

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);


greedy fails


Greedy Forwarding

Perimeter Forwarding

have left local maxima

greedy works

greedy fails

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

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

  • 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

Packet Delivery Success Rate

Routing Protocol Overhead

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

  • 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


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