XTC: A Practical Topology Control Algorithm for

Ad-Hoc Networks

Roger WattenhoferAaron Zollinger

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Overview

• What is Topology Control?

• Context – related work

• XTC algorithm

• XTC analysis– Worst case

– Average case

• Conclusions

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Topology Control

• Drop long-range neighbors: Reduces interference and energy!• But still stay connected (or even spanner)

Sometimes also clustering, Dominating Set construction

Not in this presentation

WMAN 2004

Overview

• What is Topology Control?

• Context – related work

• XTC algorithm

• XTC analysis– Worst case

– Average case

• Conclusions

WMAN 2004

Context – Previous Work

• Mid-Eighties: randomly distributed nodes[Takagi & Kleinrock 1984, Hou & Li 1986]

• Second Wave: constructions from computational geometry, Delaunay Triangulation [Hu 1993], Minimum Spanning Tree [Ramanathan & Rosales-Hain INFOCOM 2000], Gabriel Graph [Rodoplu & Meng J.Sel.Ar.Com 1999]

• Cone-Based Topology Control[Wattenhofer et al. INFOCOM 2000];explicitly prove several properties(energy spanner, sparse graph)

• Collecting more and more properties[Li et al. PODC 2001, Jia et al. SPAA 2003,Li et al. INFOCOM 2002] (e.g. local, planar, distance and energyspanner, constant node degree [Wang & Li DIALM-POMC 2003])

But: exact nodepositions known

Only neighbor directionand relative distance

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K-Neigh (Blough, Leoncini, Resta, Santi @ MobiHoc 2003)

• “Connect to k closest neighbors!”• Very simple algorithm.• On average as good as others…

• Tough question: What should k be?

[Tha

nks

to P

. S

anti]

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Percolation

• Node density such that the graph is just about to become connected(about 5 nodes per unit disk).

• What’s the value for k at percolation?!? (Tough question?)

too sparse too densecritical density

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• What if the network looks like this:

• Does a typical/average network (or parts of an average network) really look like this? Probably not… but…

• Still, cool simulation and analysisresults by Blough et al.– For example: energy to compute

K-Neigh topology is much smaller than CBTC topology (figure right)

K-Neigh and the Worst Case?

k+1 nodes k+1 nodes

Ene rgy cos t - Phas e 1 only

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Overview

• What is Topology Control?

• Context – related work

• XTC algorithm

• XTC analysis– Worst case

– Average case

• Conclusions

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XTC Algorithm

• Each node produces “ranking” of neighbors.

• Examples– Distance (closest)– Energy (lowest)– Link quality (best)

• Not necessarily depending on explicit positions

• Nodes exchange rankings with neighbors

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XTC Algorithm (Part 2)

• Each node locally goes through all neighbors in order of their ranking

• If the candidate (current neighbor) ranks any of your already processed neighbors higher than yourself, then you do not need to connect to the candidate.

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WMAN 2004

Overview

• What is Topology Control?

• Context – related work

• XTC algorithm

• XTC analysis– Worst case

– Average case

• Conclusions

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XTC Analysis (Part 1)

• Symmetry: A node u wants a node v as a neighbor if and only if v wants u.

• Proof:– Assume 1) u v and 2) u v

– Assumption 2) 9w: (i) w Áv u and (ii) w Áu v

Contradicts Assumption 1)

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XTC Analysis (Part 1)

• Symmetry: A node u wants a node v as a neighbor if and only if v wants u.

• Connectivity: If two nodes are connected originally, they will stay so (provided that rankings are based on symmetric link-weights).

• If the ranking is energy or link quality based, then XTC will choose a topology that routes around walls and obstacles.

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XTC Analysis (Part 2)

• If the given graph is a Unit Disk Graph (no obstacles, nodes homogeneous, but not necessarily uniformly distributed), then …

• The degree of each node is at most 6.• The topology is planar.• The graph is a subgraph of the RNG.

• Relative Neighborhood Graph RNG(V):• An edge e = (u,v) is in the RNG(V) iff

there is no node w with (u,w) < (u,v) and (v,w) < (u,v).

vu

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Unit Disk Graph XTC

XTC Average-Case

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XTC Average-Case (Degrees)

XTC avg

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XTC Average-Case (Stretch Factor)

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Network Density [nodes per unit disk]

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GG vs. UDG – Energy

XTC vs. UDG – Energy

GG vs. UDG – Euclidean

XTC vs. UDG – Euclidean

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Network Density [nodes per unit disk]

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XTC Average-Case (Geometric Routing)

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GOAFR+ on GG

GOAFR+ on GXTC

GFG/GPSR on GG

connectivity rate

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Conclusion

• Even with minimal assumptions, only neighbor ranking,it is possible to construct a topology with provable properties:

– Symmetry

– Connectivity

– Bounded degree

– Planarity

Simple algorithm

No complex assumptions

XTC lends itself topractical implementation+

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Topology Control

• Drop long-range neighbors: Reduces interference and energy!• But still stay connected (or even spanner)

Really?!?

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What Is Interference?

• Model– Transmitting edge e = (u,v) disturbs all nodes in vicinity

– Interference of edge e = # Nodes covered by union of the two circles with center u and v, respectively, and radius |e|

• We want to minimize maximum interference!

• At the same time topology must beconnected or a spanner etc. 8

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Low Node Degree Topology Control?

• Most researchers argue that low node degree is sufficient for low interference!

• This is not true since you can construct very bad topologies with minimum node degree but huge interference!

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Let’s Study the Following Topology!

• …from a worst-case perspective.

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Topology Control Algorithms Produce…

• All known topology control algorithms (XTC too!) include the nearest neighbor forest as a subgraph, and produce something like this:

• The interference of this graph is (n)!

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But Interference…

• Interference does not need to be high…

• This topology has interference O(1)!!

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Interesting Research Question

• We have some preliminary results:– There is no local algorithm that finds a good interference topology

– The optimal topology will not be planar, etc.

– LISE, LLISE algorithms

– [Burkhart, von Rickenbach, Wattenhofer, Z. @ MobiHoc 2004]

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Simulation

UDG, I = 50 XTC, I = 25

LLISE2, I = 23 LLISE10, I = 12

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Conclusion

• Even with minimal assumptions, only neighbor ranking,it is possible to construct a topology with provable properties:

– Symmetry

– Connectivity

– Bounded degree

– Planarity

Simple algorithm

No complex assumptions

XTC lends itself topractical implementation+

But does Topology Control really reduce interference?

Questions?Comments?

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