GLIDER: Gradient Landmark-Based Distributed Routing for Sensor Networks. Stanford University. HP Labs

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1 GLIDER: Gradient Landmark-Based Distributed Routing for Sensor Networks Qing Fang Jie Gao Leonidas J. Guibas Vin de Silva Li Zhang Stanford University HP Labs

2 Point-to-Point Routing in Sensornets Routing on geographic coordinates Only works in 2-D space Sensitive to location inaccuracy Routing on virtual coordinates Requires global embedding of the link connectivity graph in the plane Forcing a 2-D layout on a 3-D deployment may ignore much of the actual connectivity

3 Our Approach Routing on virtual coordinates, but without global embedding Works by separating the global topology and the local connectivity Partition the field into tiles. Build a light-weight, stable global routing infrastructure on these tiles using topological information. Relatively stable global topology affords proactive global route planning. Within each tile, sensor distribution is relatively nice so that greedy forwarding on local coordinates is likely to work well. Local routing uses reactive protocols based on local connectivity

4 Topological Information a 1. Reflects connectivity 2. Stable b

5 GLIDER the Basics Given a communication graph on sensor nodes, with path length in shortest path hop counts Select a set of landmarks Construct Landmark Voronoi Complex (LVC) Construct Combinatorial Delaunay Triangulation (CDT) graph on landmarks

6 Theorem: If G is connected, then the Combinatorial Delaunay graph D(L) for any subset of landmarks is also connected. 1. Compact 2. Each edge in D(L) is relatively stable 3. Each edge can be mapped to a path that uses only the nodes in the two corresponding Voronoi tiles; Each path in G can be lifted to a path in D(L)

7 Local Routing with Global Guidance Global Guidance the D(L) that encodes global connectivity information is accessible to every node for proactive route planning on tiles. Local Routing high-level routes on tiles are realized as actual paths in the network by using reactive protocols.

8 Information Stored at Each Node The shortest path tree on D(L) rooted at its home landmark The predecessors on the shortest path trees rooted at its reference landmarks A bit to record if the node is on the boundary of a tile Its coordinates and those of its neighbors for greedy routing

9 GLIDER -- Routing 1. Global planning 2. Local routing Inter-tile routing u 1 u 2 u 3 q Intra-tile routing p

10 Local Coordinates and Greedy Routing L5 L1 Reference landmarks: L 0, L k T(p) = L 0 L4 p L3 L0 q L2 Let s = mean(pl 2 0,, pl 2 k ) Local virtual coordinates: c(p)= (pl 2 0 s,, pl 2 k s) (centered metric) Distance function: d(p, q) = c(p) c(q) 2 Greedy strategy: to reach q, do gradient descent on the function d(p, q)

11 Local Landmark Coordinates No Local Minimum Theorem: In the continuous Euclidean plane, gradient descent on the function d(p, q) always converges to the destination q, provided that there are at least three non-collinear landmarks. In the discrete case, we empirically observe that landmark gradient descending does not get stuck on networks with reasonable density (each node has on average six neighbors or more).

12 u 3 u 1 u 2 q p

13 Simulations Path Length and Load Balancing GLIDER GPSR Each node on average has 6 one-hop neighbors.

14 Simulations Hot Spots Comparison Randomly pick 45 source and destination pairs, each separated by more than 30 hops. GLIDER GPSR Blue (6-8 transit paths), orange (9-11 transit paths), black (>11 transit paths)

15 GLIDER Summary A topology-enabled naming and routing scheme that based purely on link connectivity information Works by separating the global topology and the local connectivity Use topological information to build a routing infrastructure Propose a new coordinate system for a node based on its hop distances to a subset of landmarks Advantages takes only connectivity graph as input infrastructure (CDT) is lightweight routing is efficient and local

16 Future Work Criteria and algorithms for landmark selection Better methods for load balancing Potential multi-resolution LVC hierarchies

17 Examples Each node on average has 6 one-hop neighbors.

18 Naming/Addressing and Routing Encoding global information for proactive routing IP Geographical location Distance to a selected subset of landmarks

19 CDT Preserves Connectivity Definitions: Voronoi cell For a graph G = (V, E) and a subset of landmarks L V, define the Voronoi cell T(v) of a node v L to be the set of nodes whose nearest landmark is v. CDT The edge v 1 v 2 belongs to D(L) iff there exist nodes w 1, w 2 with a direct edge between w 1 and w 2 and w i T(vi), for i=1,2. Theorem: If G is connected, then the CDT graph D(L) for any subset of landmarks L is also connected.

20 Node Density vs. Success Rate of Greedy Routing 2000 nodes distributed on a perturbed grid. Perturbation ~ Gaussian(0, 0.5r), where r is the radio range

21 Topological Information Reflects connectivity Stable Compact