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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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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


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


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


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


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


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


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


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


MPR-based Pruning Techniques for Shortest Path Tree Computation

IEEE SoftCOM 2010

7

1

7

1

1

2

3

2

3

6

6

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.


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


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


  • 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


    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}


    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)


    MPR-based Pruning Techniques for Shortest Path Tree Computation

    IEEE SoftCOM 2010

    2

    1

    1

    4

    1

    3

    1

    3

    3

    1

    1

    5

    6

    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)


    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}


    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}


    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


    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)


    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)


    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


    MPR-based Pruning Techniques for Shortest Path Tree Computation

    IEEE SoftCOM 2010

    Questions ?

    E-mail: [email protected]


    MPR-based Pruning Techniques for Shortest Path Tree Computation

    IEEE SoftCOM 2010

    Backup Slides


    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))


    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)


    MPR-based Pruning Techniques for Shortest Path Tree Computation

    IEEE SoftCOM 2010

    Path MPR Definitions


    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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