XTC: A Practical Topology Control Algorithm for Ad-Hoc Networks
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Transcript of XTC: A Practical Topology Control Algorithm for Ad-Hoc Networks
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
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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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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
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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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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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Network Density [nodes per unit disk]
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Network Density [nodes per unit disk]
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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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