Localized Topology Control Algorithms for Heterogeneous Wireless Networks

1. Localized Topology Control Algorithms for Heterogeneous Wireless Networks Ning Li and Jennifer C. Hou University of Illinois at Urbana-Champaign Presented by Andrew Tzakis

2. The Goal • Increase the energy efficiency and Network capacity in wireless ad hoc networks and wireless sensor networks.

3. How to Reach this Goal • Create a topology control algorithm to improve energy efficiency and network connectivity. • Modify each node to use the lowest transmission power that will maintain the same level of network connectivity. • Benefits: • Energy efficiency will obtained by not transmitting at max power. • Spatial reuse and mitigate MAC-level contention will both be improved. • Connectivity preserved.

4. Related work • Most of the current algorithms assume Homogeneous Networks. • This is not realistic, even identical radios can have different ranges. • Rodoplu and Meng (R&M) can work on Heterogeneous network • But is later shown to not be as efficient. • Also the resulting topology is sensitive to the model used in computation.

5. Proposed Solutions • Li and Hou propose two localized topology control algorithms for heterogeneous wireless mutli-hop networks. • Directed Relative Neighborhood Graph (DRNG) • Directed Local Spanning Subgraph (DLSS)

6. Characteristics of DRNG and DLSS • DRNG and DLSS derive topologies with Smaller average node degress (both logical and physical. • Reduces MAC level contection (for better throughput). • They also produce smaller average link lengths while maintaining network connectivity. • Smaller link lengths implies smaller transmission power needed (creating better efficiency).

7. What needs to be proved • Li and Hou prove the following: • The topology derived under DRNG or DLSS preserves network connectivity. • The out-degree of any node in the topology by DLSS or DRNG is bounded by a constant. • The topology generated by DRNG or DLSS preserves network bi-directionality.

8. How DRNG and DLSS work • Information Collection • Each node locally collects the information of the neighborhood. • Topology Construction • Each node creates a proper set of neighbors for the final topology using information from step 1. • Construction of topology with only bi-directional links (optional) • Each node adjusts its set of neighbors to make sure all edges are reachable.

9. Information Collection • Each node needs to know all of the edges in its neighborhood.

10. Information Collection (2) • This can be found by having all nodes broadcast using is maximal power a hello message that has a unique node id and its max transmit power. • After each node collects its reachable neighborhood, it can broadcast this information so that each node has E(GR)for the whole graph. • This is needed for the next step, topology construction.

11. Weight Function 2 1 u1 v2 5 5 3 v1 u2

12. Topology Construction DRNG

13. Topology Construction DLSS 3:If there is no path then add it 6:Once all paths have been reconnected, stop. An example will be shown in a few slides.

14. Topology with Only Bi-Directional Links • Some links can be uni-directional in GDLSSand GDRNG. • Can apply either Addition or removal to obtain bi-directional topologies. v2 v3 v3 v1

15. Addition And Removal • Addition • Add an extra edge (v,u) into GA if (u,v)E(GA), (v,u)  E(GA), and d(v,u)  RV. • Removal • Delete any edge (u,v)E(GA) if (v,u)  E(GA)

16. The Proof • From earlier we need to prove • The topology derived under DRNG or DLSS preserves network connectivity. • The out-degree of any node in the topology by DLSS or DRNG is bounded by a constant. • The topology generated by DRNG or DLSS preserves network bi-directionality. • Assumptions: • G is always strongly connected.

17. Connectivity

18. : Stop p reaches all nodes Not Added Connectivity (2) Example of DLSS 10 u p u v 5 ADD 6 p 5 6 v ADD v p u 10

19. Connectivity (3) GDRNG says p must exist for (u,v) not to be in the graph. However, if p exists then (u,v) would not be in GDLSS

20. Bi-directionality • There exist graphs which are not bi-direction • This can occur when maximum transmission ranges are non-uniform. • Prove that DLSS or DRNG preserves bi-directionality if it exists from the beginning

21. Bi-directionality(2)

22. Degree Bound • The out-degree of a node u under algorithm A is denoted as degAout(u) is the number of out-neighbors. • The in-degree of u under algorithm A is denoted as degAin(u) is the number of in-neighbors.

23. Out Degree Bound • This is true because we know v has to at least transmit at rmin. • If there was a node inside the range then an out neighbor of u to that node would not exist since v would have a shorter weight to that node.

24. Out Degree Bound (2) • To pack the nodes as densely as we can, we will assume the worst case when all other nodes transmit at rmin. • For links a and b to exist in DLSS or DRNG a b  c. • The most dense packing would make them all equal yielding an equilateral triangle. • Angle wiuwj must be  /3 • By induction we can prove there can only be 6 such slices

25. Out Degree Bound (3) • Worst case outside the disk of rmin • All nodes transmit at rmin and are rmin/2 away from each other • u is at rmax

26. Out Degree Bound (4) • By taking the area defineed by area(rmax + rmin/2) minus the inter circle, and divide that by the rmin/2 circle area we get the max number outside the rmin/2 circle. • Note the 6 is from the inter circle

27. Out Degree Bound (5) • We can get a tighter bound on the area using hexagons.

28. In Degree Bound • In degree is similar to the inter circle, if you try to add a node p anywhere around the outside,the outside node would become the in node for p.

29. Simulation Study 1 • 50 Nodes uniformly distributed in 1000m x 1000m area with transmission range of 200m,250m

30. Simulation Study 2 • Nodes varied from 100 to 300

31. Simulation Study 3

32. Conclusion • DRNG and DLSS do the following for heterogeneous networks • Preserve network connectivity • Preserve network bi-directionality • The out-degree of any node is bounded • Simulation shows that DRNG and DLSS work much better that R&M.