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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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18 th international conference on software telecommunications and computer networks

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


18 th 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


18 th international conference on software telecommunications and computer networks

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


18 th international conference on software telecommunications and computer networks

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


18 th international conference on software telecommunications and computer networks

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


18 th international conference on software telecommunications and computer networks

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


18 th international conference on software telecommunications and computer networks

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


18 th international conference on software telecommunications and computer networks

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


18 th international conference on software telecommunications and computer networks

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.


18 th international conference on software telecommunications and computer networks

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


18 th international conference on software telecommunications and computer networks

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


  • 18 th international conference on software telecommunications and computer networks

    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


    18 th international conference on software telecommunications and computer networks

    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}


    18 th international conference on software telecommunications and computer networks

    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)


    18 th international conference on software telecommunications and computer networks

    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)


    18 th international conference on software telecommunications and computer networks

    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}


    18 th international conference on software telecommunications and computer networks

    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}


    18 th international conference on software telecommunications and computer networks

    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


    18 th international conference on software telecommunications and computer networks

    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)


    18 th international conference on software telecommunications and computer networks

    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)


    18 th international conference on software telecommunications and computer networks

    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


    18 th international conference on software telecommunications and computer networks

    MPR-based Pruning Techniques for Shortest Path Tree Computation

    IEEE SoftCOM 2010

    Questions ?

    E-mail: [email protected]


    18 th international conference on software telecommunications and computer networks

    MPR-based Pruning Techniques for Shortest Path Tree Computation

    IEEE SoftCOM 2010

    Backup Slides


    18 th international conference on software telecommunications and computer networks

    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))


    18 th international conference on software telecommunications and computer networks

    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)


    18 th international conference on software telecommunications and computer networks

    MPR-based Pruning Techniques for Shortest Path Tree Computation

    IEEE SoftCOM 2010

    Path MPR Definitions


    18 th international conference on software telecommunications and computer networks

    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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