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Interference and Topology Control Does Topology Control Reduce Interference ? Feb 15, 2010 University of Freiburg H. K. Al-Hasani Seminar Ad Hoc Netzwerke Prof. Dr. Christian Schindelhauer

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1.Motivation -Interference 2.Goals desired to achieve -Spanner graph 3.Problems and study cases 4.Algorithms -LIFE-LISE-LLISE 5.Conclusion Interference and Topology Control

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Motivation How to construct the network so that : All vertices are connected.All vertices are connected. Minimum energy consuming, toMinimum energy consuming, to Extend network lifetime.Extend network lifetime. Collision handling.Collision handling. Low Interference.Low Interference.

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x y How the communication is established

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Interference Scenario: x y |x,y| refers to the transmission discs radii of x,y.|x,y| refers to the transmission discs radii of x,y. A connection will be established if both radii were identical.A connection will be established if both radii were identical. Two nodes x,y are connected if their edge is symmetric.Two nodes x,y are connected if their edge is symmetric. In this scenario 9 nodes are influenced by this communication including x and y.In this scenario 9 nodes are influenced by this communication including x and y. Interference of a node is the number of cycles in which this node is located.Interference of a node is the number of cycles in which this node is located. Cov (e) = 9

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Interference Definition: x y Given a graph G (V,E) I (G) = max (Cov (e)), e E Lowering a graphs interference is excluding all possible edges with high coverages without loosing connectivity.

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What kind of graph can guarantee that ?

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Goals Desired graph: Low interferenceLow interference ConnectivityConnectivity Spanner graphSpanner graph Planar graphPlanar graph

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Spanner graph Given a graph G(V,E) G* would be a t-spanner for V if |x,y| PG* ≤ t.|x,y| PG where t is the stretch factor The path between these pair of nodes in G* should be equal to at most the shortest path between them in the original graph G time the stretch factor t.

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Besides spanner graph, what else we need to consider ?

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SparsenessSparseness Chain of nodesChain of nodes Worst case graphWorst case graph Planar graphPlanar graph Study cases

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Sparseness If the graphs degree could be lowered, then the interference will be lowered as well...? Claim :

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Low degree graph

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Sparseness If the graphs degree could be lowered, then the interference will be lowered as well The claim doesn‘t hold, the interference of this graph is O(n). Claim :

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Chain of nodes Set of n vertices V, in between the distance grows exponentially. |x i,x i+1 |= 2 i where I {1,…,n} |x i,x i+1 | is the radius of these nodes discs : When x i,x i+1 communicate, they interfere all other nodes in range (1,…i)

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ii+1i+2i+3 2i2i2i2i

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Some approaches will choose the greedy way, i.e. connect the nearest neighbor. Minimum Spanning Tree, or Related Neighbor Graph will push the interference of such a graph to Ω(n). i i+1 i+2i+3 Current solution : Chain of nodes

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Ask for help from the nodes in similar situation! |x i,x i+1 |= 2 i where I {1,…,n} |u i,u i+1 |= 2 i where I {1,…,n} Pick a helping node v so that: |x i,u i |< |x i,v| < |x i,u i | i i+1 i+2i+3 Suggested solution : Chain of nodes

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Constant interference u i+1 x i+1 xixixixi uiuiuiuiv

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Worst case graph Given a graph G (V,E) The vertices are located equally to each other. Except two nodes x,y : |x,y| > |u,v| where { u,v V } For connectivity reason, this edge must be set. The edge |x,y| increases the interference. x ya

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Planar graph A Planar graph, is a graph in which no two edges intersect. Planarity doesn‘t have to increase / decrease graphs interference. Our desired graph might be a planar one. a b ab a,b are small groups of nodes

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Then how can the optimal graph be constructed ?

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Algorithms LIFELIFE LISELISE LLISELLISE Algorithms

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LIFE Low Interference Forest Establisher Hence the algorithm constructs Minimum Spanning Trees, the constructed graph is a forest. If two nodes in range of each other, pick the edge with minimum coverage. Input : Set of vertices, no more requirements. Running time : O (n 2 log n)

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c b e a f gd a3b2 c2 d3 e4 f3 g5 Simulating LIFE Given a set of vertices and their maximum transmission radius:

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e g c b a fd The connectivity is violated. There are three MST, which are not connected. c b e a f g d e g c b a f d Then the constructed graph would look like … Simulating LIFE

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LISE Low Interference Spanner Establisher The algorithm constructs Spanner graph. Shortest path is computed separately. Low weighted (low coverage) edges are inserted to the graph. Input : Set of vertices, Stretch factor (t). Running time : polynomial.

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LLISE Local Low Interference Spanner Establisher The algorithm applied locally for edge e. Search within t/2 neighbors for eligible paths. Find the optimal interference path among these paths. Inform the neighbors to use this path only. Input : Set of vertices, stretch factor.

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Conclusion 1.Stretch factor For some kind of graphs, stretch factor is known. Compute the stretch factor considered to be very expensive. 2.Networks knowledge Either to find the neighbors, or to find the shortest path. In LIFE it is required to set the edge with minimum coverage. LISE and LLISE are a good start although certain information is required :

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Conclusion 3.Shortest path computation The running time of the algorithms depends on the implementation of this point. The proofs trigger many arguments! Algorithms performance is close to the optimal if the stretch factor has large value. Nevertheless for small values the algorithms performance doesn’t differ from Related neighbor Graphs.

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Does Topology Control Reduce Interference Martin Burkhart, Pascal von Rickenbach, Roger Wattenhofer, Aaron Zollinger Energy, Congestion and Dilation in Radio Networks Friedhelm Meyer auf der Heide, Christian Schindelhauer, Klaus Volbert, Matthias Grünewald Analysis of Interference in Ad-Hoc Networks Martin Burkhart Spanner Graph based Topology Aggregation Schemes for Large Networks Aniruddha S. Diwan, P. Basker, Kumar N. Sivarajan Constructing Interference-Minimal Networks Marc Benkert, Joachim Gudmundsson, Herman Haverkort, Alexander Wolff Improved Randomized Algorithms for Path Problems in Graphs Surender Baswana Geometric Spanners Joachim Gudmundsson, Giri Narasimhan, Michiel Smid A Robust Interference Model forWireless Ad-Hoc Networks Pascal von Rickenbach, Stefan Schmid, Roger Wattenhofer, Aaron Zollinger Low-Interference Topology Control for Wireless Ad Hoc Networks Kousha Moaveni-Nejad and Xiang-Yang Li Improving the stretch factor of a graph by edge augmentation Mohammad Farshi, Panos Giannopoulos, Joachim Gudmundsson Location-based Routing in Ad hoc Networks Lecture notes GRAPH SPANNERS Lecture notes by: S.Nithya On the Locality of Distributed Sparse Spanner Constructions Lecture notes by: B. Derbel, C. Gavoille, D. Peleg, L. Viennot Thank you!

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