Geographic Routing Without Planarization Ben Leong, Barbara Liskov & Robert Morris Require Planarization

MIT CSAIL

Geographic Routing without Planarization Ben Leong, Barbara Liskov & Robert Morris require planarization

Tree Routing (GDSTR) DOES NOT uses spanning tree, not planar graph low maintenance cost better routing performance than existing algorithms – – – –

Greedy Distributed Spanning New geographic routing algorithm • Overview Background Problem Approach Simulation Results Conclusion • • • • • x-y coordinates

x-y

Geographic Routing can use virtual coordinates (Rao et al. 2003) – Wireless nodes have Nodes know coordinates of immediate neighbors Packet destinations specified with coordinates In general, forward packets greedily • • • • Geographic Routing Geographic Routing Source Destination

Geographic Routing Source Destination

Greedy Forwarding Source Destination

Greedy Forwarding Source Destination Whoops. Dead end!

Geographic Routing:

Dealing with Dead Ends Source Destination

Face Routing Source Destination

Back to Greedy Forwarding Source Destination

Back to Greedy Forwarding Source t work ’

Planarization is Costly! GG and RNG don CLDP (Kim et al., 2005) – – Planarization is hard for real networks Planarization is complicated & costly! • • ” summarize “

Tree Routing (GDSTR) convex hulls tells us what points are possibly reachable reduces the subtree that must be traversed (smaller search problem) – – the area covered by a subtree Greedy Distributed Spanning Route on a spanning tree Use convex hulls to • • Hull Tree Hull Tree Destination

GDSTR Example Source Destination

Revert to Greedy Forwarding Source Destination

Revert to Greedy Forwarding Source Issues multiple hull trees conflict Hulls – – Choosing forwarding direction Undeliverable packets • • Destination

Using Multiple Trees Source Destination direction.

Using Multiple Trees Source ” bad With one tree, may be forced to route in “ Destination a void ” approximate “

Using Multiple Trees Source Two extremal-rooted trees are usually sufficient to Destination

Using Multiple Trees Source Pick tree with root closest to the destination Summary: Routing choose tree record start node traverse subtree – – – Try greedy forwarding Dead end: If possible, revert to greedy forwarding Back to start node: packet undeliverable • • • • . t s to

Theorem in connected graph t , GDSTR guarantees

Given a pair of nodes G and packet delivery from messages

keepalive

Building Hull Trees minimal and maximal x-coordinates minimal hop count from root – – Choose roots: Convex hull info in Want compact trees Aggregate convex hulls from leaves to root Conflict hull info percolates from root to leaves • • • • • )

Simulation Results low/high density low/high obstacle density • • average node degree Path Stretch Hop Stretch range of network densities ( larger networks up to 5,000 nodes – – – – Measured 2 routing metrics: Topologies • • Simulation Results GPSR (Karp, 2001), GOAFR+ (Kuhn, 2003) and GPVFR (Leong et al., 2005) storage bandwidth – – – – – Compare with Measured costs and compared with CLDP: • under CLDP planarization (Kim et al., 2005) • Hop Stretch Hop Stretch O(log n) s scan] ’

Costs convex hull computation: operations [Graham – Computation: Storage: < 1 kb Bandwidth • • • Message Sizes Messages for Startup Messages for Stabilization up to 20% better Summary – Maintenance cost one order of magnitude less than CLDP (face routing) Better routing performance (stretch) • • Large Voids Small Voids Destination Source

Explaining Performance Destination Source

Explaining Performance Extra overhead Summary

• Sparse networks – GDSTR chooses correct forwarding direction more often than face routing • Moderately dense networks – Faces are small, forwarding direction is inconsequential – Trees do not “approximate” small voids well • Ultra-dense networks – Greedy forwarding works all the time! Conclusion information allows GDSTR ” Global to choose good forwarding direction more often GDSTR achieves improved routing stretch at lower maintenance cost than CLDP Cheaper to maintain two hull trees than a planar graph “ • • • Future Work convex hulls generalizable to higher dimensions – Evaluate GDSTR in a practical and mobile setting Geographic routing in higher dimensions • • MIT CSAIL

Geographic Routing without Planarization Ben Leong, Barbara Liskov & Robert Morris Reducing Convex Hulls Reducing Convex Hulls Reducing Convex Hulls allow us to avoid

Conflict Hulls : parent nodes tell child Undeliverable packets will be forwarded to the root. forwarding to the root Conflict hulls Key idea about other nodes with intersecting hulls • • • Example: Conflict Hull Example: Conflict Hull Example: Conflict Hull Example: Conflict Hull Example: Conflict Hull …

Example: Conflict Hull Forward to parent Example: Conflict Hull Packet undeliverable! Minimal-x Tree Maximal-x Tree

Example GDSTR Hull Trees Two Trees

Topologies

Comparing Routing (CLDP) Planar Graph