Path Vector Face Routing: Geographic Routing with Local Face - - PowerPoint PPT Presentation

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Path Vector Face Routing: Geographic Routing with Local Face - - PowerPoint PPT Presentation

Apr 09, 2023 206 likes •847 views

Path Vector Face Routing: Geographic Routing with Local Face Information Ben Leong, Sayan Mitra, and Barbara Liskov MIT CSAIL Geographic Routing Geographic routing algorithms leverage physical location information scale better

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Path Vector Face Routing: Geographic Routing with Local Face Information

Ben Leong, Sayan Mitra, and Barbara Liskov MIT CSAIL

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SLIDE 2

Geographic Routing

  • Geographic routing algorithms

– leverage physical location information – scale better than other ad hoc routing algorithms (Karp, 2001) – state proportional to network density, not size – can be applied using virtual coordinates (Rao et al., 2003)

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Geographic Routing

  • Existing geographic routing algorithms

– GPSR (Karp, 2001) GFG (Bose, 2001) – GOAFR+ (Kuhn, 2003) – nodes know only about immediate neighbors

  • Can we do better if nodes have more

information?

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SLIDE 4

Geographic Routing

  • Existing geographic routing algorithms

– GPSR (Karp, 2001) GFG (Bose, 2001) – GOAFR+ (Kuhn, 2003) – nodes know only about immediate neighbors

  • Can we do better if nodes have more

information? Yes!

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Greedy Path Vector Face Routing

  • Our new algorithm (GPVFR):

– stores small amount of additional local information (< 200 bytes) – improve maximum routing stretch over GPSR by 35 to 40% – improve maximum routing stretch over GOAFR+ by 20 to 25%

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SLIDE 6

Overview

  • Problem
  • Approach
  • Simulation Results
  • Conclusion
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Geographic Routing

  • Nodes have x-y coordinates
  • Nodes know coordinates of immediate

neighbors

  • Packet destinations specified with x-y

coordinates

  • In general, forward packets greedily
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Example

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Example

Source

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Example

Destination Source

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SLIDE 11

Example

Source Destination

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SLIDE 12

Example

Source Destination

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Example

Source Destination

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Example

Source Destination

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Geographic Face Routing

  • Problem: sometimes a packet ends up at a local

minimum.

  • Face routing – route packet along faces of a

planar subgraph

  • Planarization:

– Relative Neighborhood Graph (RNG) – Gabriel Graph (GG) – Cross Link Detection Protocol (CLDP) (Kim et al., NSDI 2005)

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Example

Source Destination

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Example

Source Destination

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Example

Source Destination

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SLIDE 19

Example

Source Destination

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SLIDE 20

Example

Source Destination

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Example

Source Destination

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Example

Source Destination

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Problem

Nodes do not know enough to determine the“correct” forwarding direction.

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Bad Choice Example

Destination Source

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Bad Choice Example

Destination Source

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Bad Choice Example

Destination Source

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Hypothesis

By maintaining several hops of information along each planar face, we can make a better choice when deciding how to traverse a face

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Greedy Path Vector Face Routing (GPVFR)

  • Three modes:
  • 1. Forward greedily if possible.
  • 2. Use face information to forward along

existing face

  • 3. Fallback on face traversal (GPSR)
  • Revert to greedy forwarding as soon as it

is feasible

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Using Face Information

Source Destination

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Using Face Information

Source Destination

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Revert to Greedy Mode

Source Destination

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Path Vector Exchange (PVEX)

  • Protocol for maintaining face

information

  • Nodes periodically exchange path

vectors with planar neighbors

– h hops of information

  • Information is piggybacked on

keepalive messages

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Maintaining Face Information

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Maintaining Face Information

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Simulation Results

  • Measured 2 routing metrics:

– Path Stretch – Hop Stretch

  • Random networks over a range of network

densities

  • Compare to GPSR (Karp, 2001) and GOAFR+

(Kuhn, 2003)

  • Results for RNG and GG planarization in paper
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Hop Stretch (CLDP Planarization)

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Hop Stretch (CLDP Planarization)

Average node degree 9

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Scaling up

Average node density = 9

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Hop Stretch (CLDP Planarization)

Average node degree 8

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Scaling up

Average node density = 8

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Scaling up

Average node density = 7

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Scaling up

Average node density = 6.5

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Varying Path Vector Length

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Maintenance Cost

  • Additional storage:

– Small (15 to 20 extra nodes on average, < 200 bytes) – proportional to number of planar neighbors – independent of network density

  • Additional bandwidth:

– h message exchanges (each < 200 bytes)

  • Planarization cost >> PVEX cost
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Theoretical results

  • 1. With full face information, we

can route obliviously;

  • 2. Without full face information, it

is impossible to route

  • bliviously.
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Conclusion

  • Forwarding direction is critical

for good performance

  • GPVFR achieves significantly

improved routing stretch with a little extra storage.

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Path Vector Face Routing: Geographic Routing with Local Face Information

Ben Leong, Sayan Mitra, and Barbara Liskov MIT CSAIL

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Why unlimited face information can be bad

Source Destination

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Why unlimited face information can be bad

Source Destination

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Why unlimited face information can be bad

Source Destination

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Why unlimited face information can be bad

Source Destination

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SLIDE 52

Why unlimited face information can be bad

Source Destination

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SLIDE 53

Why unlimited face information can be bad

Source Destination

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Why unlimited face information can be bad

Source Destination

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Why unlimited face information can be bad

Source Destination

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SLIDE 56

Why unlimited face information can be bad

Source Destination

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Theorem 1

Given a connected pair of nodes v and t in a planar graph G, assuming that every node in G completely knows all its faces, we can route from v to t

  • bliviously
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Theorem 1 Paraphrased

With full face information at each node, we can route without storing state in the packets

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Oblivious Routing with Full Face Information (OPVFR)

  • Suppose all nodes have full face

information

  • Do:

– Find target node and route towards it. – To find target node: find edge that is nearest to destination node among all faces. Node on edge that is nearer destination is target node.

  • Break ties in some consistent way.
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Non-oblivious Routing

  • Need to know when we come back to the same

node!

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Non-oblivious Routing

  • Need to know when to switch back to greedy
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Theorem 2

For any given non-negative integer h, there does not exist a deterministic oblivious routing algorithm that guarantees packet delivery for all planar graphs if nodes are limited to knowing only about nodes that are up to h hops away

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Theorem 2 Paraphrased

If nodes do not have full face information, it is impossible to always route correctly without storing some state in the packets.