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IEEE SoftCOM 2010 Bol (Brac), 23-25 September 2010. MPR-based Pruning Techniques for Shortest Path Tree Computation. Juan Antonio Cordero Équipe Hipercom -- INRIA Saclay (France). 18 th International Conference on Software Telecommunications and Computer Networks.

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slide1

IEEE SoftCOM 2010

Bol (Brac), 23-25 September 2010

MPR-based Pruning Techniques for Shortest Path Tree Computation

Juan Antonio Cordero

Équipe Hipercom -- INRIA Saclay (France)

18th International Conference on Software Telecommunications and Computer Networks

slide2

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

  • Motivation

Agenda

  • Motivation
  • Topology Pruning in Link State Routing
  • MPR for Topology Pruning
  • Path MPR
  • Impact of the Path MPR Modification
slide3

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Motivation (1)

Flooding in Wireless Ad hoc Networks

  • Pure flooding
    • Redundant retransmissions
    • Collisions
    • Reduction of effective bandwidth
  • Multi-Point Relaying (MPR)
    • Only a subset of the neighbors are allowed to relay (forward) a message
slide4

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Motivation (2)

Multi-Point Relays (MPR)

MPR coverage criterion

Every 2-hop neighbor of the source is covered by (at least) one relay

slide5

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

  • Topology Pruning in Link State Routing

Agenda

  • Motivation
  • Topology Pruning in Link State Routing
  • MPR for Topology Pruning
  • Path MPR
  • Impact of the Path MPR Modification
slide6

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Topology

Advertisement 1

Topology

Advertisement 2

Topology

Acquisition

Shortest Path Tree

Computation

.

.

.

Topology

Advertisement n

Topology Pruning

Topology Pruning in Link State Routing

  • Link State Routing
  • Wireless ad hoc networks  Scarce and shared BW
    • Not all links are necessary for Shortest Paths computation
slide7

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

  • MPR for Topology Pruning

Agenda

  • Motivation
  • Topology Pruning in Link State Routing
  • MPR for Topology Pruning
  • Path MPR
  • Impact of the Path MPR Modification
slide8

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Topology

Advertisement 1

Topology

Advertisement 2

Topology

Acquisition

Shortest Path Tree

Computation

.

.

.

Resulting overlay

Topology

Advertisement n

MPR for Topology Pruning (1)

Requirements

Rest of the network

Computing node

  • Requirements for the resulting overlay:
    • Connection
    • Preservation of Shortest Paths
slide9

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

7

1

7

1

1

2

3

2

3

6

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4

5

4

5

8

8

MPR for Topology Pruning (2)

Overlay Connection

  • The overlay of links connecting nodes to their MPRs is NOT necessarily connected.
    • Every connected component is dense.
  • The overlay of links connecting nodes to their MPRs together with all the links of ANY node in the network IS ALWAYS connected.
slide10

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

MPR for Topology Pruning (3)

Preservation of Shortest Paths

(from a node s)

The local shortest path between two nodes x and y, reachable in 2 hops,

is the path in 2 or less hops between x and y with minimal cost.

local reverse shortest path to x

network-wide direct shortest path from s

4

2

network

1

min.cost

3

1

x

s

2

7

2

For an overlay that includes all links from s,

Preservation of links to 1-hop neighbors providing local reverse shortest paths to x, x

Preservation of network-wide direct shortest paths from s

slide11

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

MPR for Topology Pruning (and 4)

Summary of Results

  • Overlay of MPR links
    • Not necessarily connected.
    • Dense for each connected components.
  • Connected overlay including links from a single node s
    • For every node x, preserves local reverse shortest paths to x
    • Preserves network-wide direct shortest path from s
slide12

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

  • Path MPR

Agenda

  • Motivation
  • Topology Pruning in Link State Routing
  • MPR for Topology Pruning
  • Path MPR
  • Impact of the Path MPR Modification
slide13

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Path MPR (1)

Selection of links to advertise

  • Specified in RFC 5449

Path MPR Selection

Cost-Coverage

Translation

MPR Selection

N(x)

N2(x)

N’(x)

N2’(x)

PathMPR(x)

  • N’(x) = {1-hop neighbors of x for which the direct link from x is locally optimal}
  • N2’(x) = {1-hop and 2-hop neighbors of x for which the local shortest path to x
          • has 2 hops}
slide14

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

  • Connection:
  • Preservation of local reverse shortest paths:

Path MPR (2)

Resulting Overlay

  • Specified in RFC 5449
  • For a node s of the network, the Path MPR overlay consists of:
  • N(s)
  • x in the network, links from x to PathMPR(x)
slide15

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

2

1

1

4

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3

1

1

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Path MPR (3)

(Non) Preservation of shortest paths

  • Example of non-preservation of shortest paths with general costs

N(1)

N2(1)

N’(1)

N(1) = {2, 3, 6}

N2(1) = {4, 5}

N’2(1)

N’(1) = {2, 3}

N’2(1) = {4, 5}

PathMPR(1) = {3}

Shortest_Path(41) = 4-2-1

  • (with unit costs shortest paths are always preserved)
slide16

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Path MPR Selection

N(x)

N2(x)

E2x

N’(x)

N2’(x)

E2x’

Cost-Coverage

Translation

MPR Selection

PathMPR(x)

Path MPR (4)

Proposed correction

  • Idea: exclude links not participating in shortest paths

(E2x)’ = {Links taking part in local reverse shortest paths to x}

slide17

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

N’(1)

2

1

2

1

1

1

4

4

N’2(1)

1

1

3

1

3

3

1

3

3

1

1

3

1

1

5

6

5

6

Path MPR (and 5)

Proposed correction

  • Application on the example

N(1) = {2, 3, 6}

N2(1) = {4, 5}

N’(1) = {2, 3}

N’2(1) = {4, 5}

(E2x)’ = E2x \ {(6,1), (4,3)}

PathMPR(1) = {2, 3}

slide18

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

  • Impact of the Path MPR Modification

Agenda

  • Motivation
  • Topology Pruning in Link State Routing
  • MPR for Topology Pruning
  • Path MPR
  • Impact of the Path MPR Modification
slide19

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

A first impact estimation (1)

Distance-based costs

+

Proposed modification

Path MPR (RFC 5449)

slide20

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

A first impact estimation (2)

Random costs

+

Proposed modification

Path MPR (RFC 5449)

slide21

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Conclusions & Future Work

  • General contributions
    • Conditions for a distributed topology pruning algorithm
    • Characterization of the MPR overlay: density, connection and preservation of shortest paths
  • Analysis of the Path MPR algorithm (RFC 5449)
    • Sub-optimality in non-unitary metrics
    • Proposed correction: proof of correctness and impact evaluation in static ideal network graphs
  • Future Work
  • Implementation and evaluation in more realistic ad hoc deployments, with different (non-hop) metrics
slide22

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Questions ?

E-mail: [email protected]

slide23

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Backup Slides

slide24

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Multi-Point Relays Heuristics

Input: x, N(x), N2(x)

MPR = {}

MPR  {n  N(x) :  m  N2(x), m only covered by n}

while ( uncovered 2-hop neighbors)MPR  n  N(x) : covers max. # of uncovered 2-hop neighbors

Output: MPR(x, N(x), N2(x))

slide25

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

1

2

3

4

(k-1)

2k-1

2k

Examples of MPR overlay disconnection

  • Example of disconnected MPR overlay in a k-diameter network (k>0)
slide26

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Path MPR Definitions

slide27

MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

Static Simulation Parameters

  • (Simulations run with Maple V)
  • Samples / experiment : 20
  • Radio range (rr) : 150 m
  • Square grid length : 400 m
  • Node distribution : Uniform
  • Mobility : Static
  • Channel model : Ideal
  • Metrics model : K = 10
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