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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

- 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

A

S

D

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

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

- 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

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

z

u

D

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

w

x

Remove Crossing Edge

z

u

D

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

w

x

- 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

RNG

- RNG is a sub-graph of GG
- Because RNG removes more edges

- If the original graph isconnected, RNG is also connected

GG

w

- 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

u

v

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

- 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);

}

- if (mode == greedy) {

greedy fails

Greedy Forwarding

Perimeter Forwarding

have left local maxima

greedy works

greedy fails

- 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

- 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

- 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