A Unified Energy Efficient Topology for Unicast and Broadcast

1. A Unified Energy Efficient Topology for Unicast and Broadcast Xiang-Yang Li*, Wen-Zhang Song†andWeiZhao Wang* *Illinois Institute of Technology †Washington State University, Vancouver xli@cs.iit.edu

2. Organization • Introduction • Topology control • Preferred properties • Unified Structure • Unicast • Broadcast • Conclusion and Future Works

3. Routing • Metric Based Routing • DSR, AODV, …. • Location Based Routing • GPSR, GFG, AFR,…. • Content Based Routing

4. Metric Based Routing • Link Metric Based • Each link has a cost, then need to find a path with the minimum link cost • Shortest path in O(m+n log n) time • A sparse structure with m=O(n) edges • Save cost of finding routes, updating routes • But the structure needs to be power efficient • Power of the best path connecting any pair of nodes is comparable with the best path originally

5. Location Based Routing • Each node forwards message to “best” neighbor • E.g., “best”  closest to target t s

6. Greedy Routing? • Fails to delivery t ? w s What should node w do?

7. Get out of local minimum • Find a planar graph • Gabriel Graph, for example • Face Routing or Right Hand Rule t ? w s

8. Topology Control • Topology control is to select some nodes and/or some available links as candidates for routing • Backbone based structures select some nodes • Mainly used for broadcast, multicast • Typically assume that node’s power fixed • —thus minimize the number of backbone nodes (MCDS) • Flat structure select some links, e.g., GG,LMST • Used for unicast, or broadcast • Typically assume that node’s power adjustable • ---thus minimize the total power (so called low-weight), or power to connect any pair of devices (so called spanner)

9. tradeoffs What we want to achieve? • Build a single structure efficiently with a number of nice properties: • Power efficient Unicast (majority operations) • Power efficient broadcast (widely used in WSN) • Bounded node degree (logical, physical) • Planar structure (support greedy routing) • Separated neighbors (directional antenna, reduce signal interference) • All these properties are achieved in a single structure

10. What do we mean by “efficiently”? • Best scenario • Localized method (run in constant rounds) to build such structure • Our achievement • A semi-localized method with total communication cost O(n log n) bits with wireless broadcast model • Worst case still O(n) rounds

11. Our Network Model • A set V of n wireless nodes in 2D region • All nodes with same transmission radius • Ideal case,  • It induces a unit disk graph UDG • Two nodes are connected directly if distance at most one unit • Each node knows the position of its one-hop neighbors • Localization techniques assumed already in place

12. u v The Power Model • Power needed to support a link uv is proportional to • This model • Only accounts for emission power • Good only if long range communication, or techniques are used to reduce the receiving power

13. Some Proximity Structures RNG GG MST Yao

14. Unicast – Priori Arts Not exhaustive here, due to space limit

15. Algorithm Assume GG has been constructed. Once a node u has smallest ID among unprocessed neighbors, then: If it has processed neighbors, then it keeps the nearest processed neighbor and delete others conflicted with this Otherwise, it selects the nearest unprocessed neighbor and delete the conflicted neighbors and repeat till all nodes are processed Let SqGG be the final structure u v q Power Efficient Unicast Structure Q-region

16. processed unprocessed Structure Illustration e d c f b g h a i u j r k l q p m n o

17. Properties • We can prove that the resulting topology is • Planar • Power efficient for unicast • Bounded logical node degree • Neighbor q-separation • What we miss is (counter example omitted) • Power efficient for broadcast (low weight)

18. s Energy Efficient Broadcast Any broadcast can be viewed as an arborescence rooted at s

19. Priori Arts On Efficient Broadcast • Several Structures Proposed • MST, BIP, SPT, RNG, etc., • Theoretically Good • MST, BIP: within constant of optimum • But, • not localized, or even not efficient in a distributed way • Not efficient for unicast

20. Broadcast – Low-weight Optimal A structure is called low-weighted if its total link length is within O(1) of MST Proved previously: Given any low-weighted structure H, the total power consumption for broadcast is the best among all locally constructed structures

21. Add Low-Weight Property • Previous approach • Given a structure, such as RNG, LMST v u y x Remove the longest link of any quadrilateral

22. Not Efficient for Unicast Anymore May break connectivity for graph constructed previously

23. Our New Approach • Previous method removes too many edges • Remove only needed • Avoid cascade effect

24. Independent Links • Two links xy and uv are dependent • If xy or uv is the longest edge of uvyx v u y x

25. u v y x Unified Approach • Build SqGG graph • Each node x collects 2-hop links E(x) • Node x picks link xy with smallest ID (xy, maxID(x,y), minID(x,y)) • If exits uv such that xy>max(uv,3ux,3vy) • removes link xy from E(x) • Otherwise • keeps link xy forever • Let LSqGG be the final structure

26. Properties • We can prove that the resulting topology • Planar • Power efficient for unicast • Bounded logical node degree • Neighbor q-separation • Power efficient for broadcast (low weight) • Can be constructed efficiently using O(n) messages

27. Additional Properties • Interference • Dynamic Update

28. u v y x Expected Interference • Interference • The physical degree of node u I(u)=7

29. Random Deployment • When nodes are of Poisson distribution • The maximum node interference is at least O(log n) for any connected structure almost surely • Proof omitted • Thus our structures also are bad in terms of the maximum node interference

30. Random Deployment • When nodes are of Poisson distribution • The average node interference is only O(1) for the following structures • RNG, GG, LMST, SqGG, LSqGG,…..,

31. Dynamic Topology • Mobility creates a dynamic topology, i.e., • changes in the connectivity between nodes as a function of distance • Break some links, add new links • the power of their transmitters, i.e., the nodal distances (link length)

32. Conservative Update • Assume a synchronized clock,  • Node u keeps the position v’ of its neighbors v in previous time-out • In a new time-out, u does nothing if, for every neighbor v • Otherwise, it initiates topology update

33. Properties • When no update is performed, it is still • Power efficient for unicast • Power efficient for broadcast • Bounded degree • “planar” (topologically) • Separation property (need to choose parameter carefully)

34. Conclusion • In this talk, we design a unified structure • Energy efficient for unicast • “Energy efficient for broadcast” • Bounded logical degree • Bounded physical degree for random deployment • Good for directional antenna (neighbors separated) • Good for localized routing • Can be constructed using only O(n) messages total • Semi-localized

35. Future Work • Link is more probabilistic • Design efficient structures in this case • Study efficient broadcast and multicast • What is the best we can do by using a localized method? • Or, does it exist a pure localized method at all for some questions?

36. Questions and Comments

37. 3 days TaiXing 5 days ShangHai London 7 hours 14 hours 3 hours Chicago Cologne KunMing ShenZhen 6 days HongKong During past 15 days