GPSR: Greedy Perimeter Stateless
Routing for Wireless Networks
B. Karp, H. T. Kung
Borrowed some slides from Richard Yang’s
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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
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
A
D
- 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
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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
z
u
D

w
x originates a packet to u
Right-hand rule results in the
tour x-u-z-w-u-x

x
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Remove Crossing Edge
z
u
D
Make
w
the graph planar
Remove
x
(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
RNG
GG

Because RNG removes more
edges
GG
 If the original graph is
connected, RNG is also
connected
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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
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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
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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 fails
Greedy Forwarding
Perimeter Forwarding
have left local maxima
greedy 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?
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