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GPSR: Greedy Perimeter Stateless Routing for Wireless Networks

B. Karp, H. T. Kung

Borrowed slides from Richard Yang

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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

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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

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Assumptions

Every node knows its location Positioning devices like GPS Localization

A source can get the location of the destination

802.11 MACLink bidirectionality

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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

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Benefits of GF

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

Routing decisions can be dynamically made

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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

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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

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Right Hand Rule on Convex Subdivision

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

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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

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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

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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)

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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

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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

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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

RNG

GG

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Connectedness of RNG Graph

Key observation Any edge on the minimum

spanning tree of the originalgraph is not removed

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

u v

w

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• 200 nodes

• randomly placed on a 2000 x 2000 meter region

• radio range of 250 m

•Bonus: remove redundant, competing path less collision

Full graph GG subset RNG subset

Examples

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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);

}

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GPSR

Greedy Forwarding Perimeter Forwarding

greedy fails

have left local maximagreedy works greedy fails

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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

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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

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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

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Packet Delivery Success Rate

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Routing Protocol Overhead

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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

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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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Questions?