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Authors: Raissa D’Souza, David Galvin, Cristopher Moor, Dana Randall Venue: IPSN’2006

Global Connectivity from Local Geometric Constraints for Sensor Networks with Various Wireless Footprints. Authors: Raissa D’Souza, David Galvin, Cristopher Moor, Dana Randall Venue: IPSN’2006 Presentator: Yunhuai LIU. Outline. Introduction Knowledge before this paper

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Authors: Raissa D’Souza, David Galvin, Cristopher Moor, Dana Randall Venue: IPSN’2006

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  1. Global Connectivity from Local Geometric Constraints for Sensor Networks with Various Wireless Footprints Authors: Raissa D’Souza, David Galvin, Cristopher Moor, Dana Randall Venue: IPSN’2006 Presentator: Yunhuai LIU

  2. Outline • Introduction • Knowledge before this paper • Global connectivity of Gθ • Sparseness of Gθ • When will greedy routing works

  3. Adaptive Power Topology Control • Save energy by reduced transmission power • Connectivity must be preserved

  4. θ Localized Algorithms of θ-graph (Gθ) • Use local information to guarantee global connectivity • Assume location information or direction information • Θ-graph, or Gθ • Neighbor nodes divide the circle of a node to many sectors with the largest angle < θ • θ-constraint Key issue: what is the critical value of θ that can guarantee the global connectivity?

  5. What We Have Known Before • θ<5π/6 • By Wattenhofer in Infocom’01 and PODC’01 • Under unit disk model • The first proposal of APTC • θ<π • By the same author of this paper in Infocom’03 • Again, disk model • No boundary effect is considered

  6. Three Issue in This Paper • Boundary effect and various wireless footprint • The sparseness of Gθ • Geography-based routing on APTC topologies

  7. Boundary Effect • Boundary nodes and interior nodes • Special care of boundary nodes • θB--- θ of interior nodes • θI--- θ of interior nodes • Wireless footprint – in contrast with disk model

  8. Three Conclusions • Guaranteed global connectivity when: • Boundary node set is inner connected and θI< π, with any wireless footprint • θB< 3π/2, θI< π, and wireless footprint is “week-monotonicity” • θI< π and the average of footprints is approximately to be uniform disks (no θB constraint)

  9. Disk model (monotonicity) Weak-monotonicity Week-monotonicity • It is less restrictive than unit disk model • Weak-monotonicity • if {I,j} is an edge and k is a node where ∟jik = α and d(i, k) ≤ cos(α)∙d(i, j), then ~ik is also an edge.

  10. Sparseness of Gθ • How sparse is Gθ: • θ= π • The expected out-degree = 5 • Variance=4 • θ= 2π/3 • The expected out-degree = 8.875 • 12.2344

  11. Geography-based Routing • Footprint eccentricity α • Defined as the smallest constant with the property that for every u and v, if u and v are connected, then u is connect to every w such that d(u,w)<d(u,v)/ α

  12. When Will Greedy Routing FAIL? • When α<2, we can always find a θ so that by satisfying θ-constraint, the network is globally connected • When α>2, we can arrange the nodes to let greedy geography-based routing fail

  13. Question and Answer • Thanks for you patient

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