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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). 18 th International Conference on Software Telecommunications and Computer Networks.

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18 th International Conference on Software Telecommunications and Computer Networks

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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.

  10. 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

  11. 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

  12. 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

  13. 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}

  14. 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)

  15. 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)

  16. 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}

  17. 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. 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

  19. 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) 

  20. 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) 

  21. 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

  22. MPR-based Pruning Techniques for Shortest Path Tree Computation IEEE SoftCOM 2010 Questions ? E-mail: cordero@lix.polytechnique.fr

  23. MPR-based Pruning Techniques for Shortest Path Tree Computation IEEE SoftCOM 2010 Backup Slides

  24. 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))

  25. 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)

  26. MPR-based Pruning Techniques for Shortest Path Tree Computation IEEE SoftCOM 2010 Path MPR Definitions

  27. 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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