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

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

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

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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

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

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

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

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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)

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9 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 tradeoffs

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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

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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

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12 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 u v

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13 Some Proximity Structures RNGGG Yao MST

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14 Unicast – Priori Arts PlanarPower Spanner Degree Bound Communication Cost Bound RNGYesNo n GGYes Non LDelYes No~60n YaoNoYes7(2K+1)n BPSYes 27~700n OrdYaoGGYes 1224n SYaoGGYes 93n Not exhaustive here, due to space limit

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15 Power Efficient Unicast Structure 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 S GG be the final structure region u v

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

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

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

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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

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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

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

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

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

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

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25 Unified Approach Build S GG 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 LS GG be the final structure x y uv

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

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27 Additional Properties Interference Dynamic Update

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

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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

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

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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)

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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

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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)

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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

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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?

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36 Questions and Comments

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37 During past 15 days HongKong ShenZhen KunMing TaiXing ShangHai Chicago London Cologne 14 hours 7 hours 3 hours 5 days 3 days6 days

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