Conflict graphs and the SINR-capacity of the mean power scheme

The Capacity problem in wireless networks is to select a maximum cardinality feasible subset of a set of transmission requests or links, where a set of links is feasible if the corresponding transmissions can be done simultaneously without collisions. We consider two models of feasibility: the SINR (Signal to Interference and Noise Ratio) model and a special conflict graph model. We show that if a special power assignment method is used (called the mean power scheme), then the solutions of the Capacity problem in the two models differ by at most a constant factor for any set of links in a doubling metric space of small dimension. This is not true for other power assignment methods in general. This result, besides showing that the mean power scheme is scalable between different models (as opposed to other power schemes), also has the potential to yield new results in the SINR model, using tools from graph theory, which we demonstrate in several examples.

[1]  Tigran Tonoyan.  On the Capacity of Oblivious Powers , 2011, ALGOSENSORS.

[2]  Jørgen Bang-Jensen,et al.  Vertex coloring edge-weighted digraphs , 2015, Inf. Process. Lett..

[3]  Berthold Vöcking,et al.  Distributed Contention Resolution in Wireless Networks , 2010, DISC.

[4]  Roger Wattenhofer,et al.  Wireless Communication Is in APX , 2009, ICALP.

[5]  J. Heinonen.  Lectures on Analysis on Metric Spaces , 2000 .

[6]  Paolo Santi,et al.  A framework for joint scheduling and diversity exploitation under physical interference in wireless mesh networks , 2008, 2008 5th IEEE International Conference on Mobile Ad Hoc and Sensor Systems.

[7]  Magnús M. Halldórsson,et al.  Nearly Optimal Bounds for Distributed Wireless Scheduling in the SINR Model , 2011, ICALP.

[8]  Berthold Vöcking,et al.  Oblivious interference scheduling , 2009, PODC '09.

[9]  Magnús M. Halldórsson.  Wireless scheduling with power control , 2012, TALG.

[10]  Martin Hoefer,et al.  Scheduling in Wireless Networks with Rayleigh-Fading Interference , 2015, IEEE Transactions on Mobile Computing.

[11]  Roger Wattenhofer,et al.  Protocol Design Beyond Graph-Based Models , 2006, HotNets.

[12]  Roger Wattenhofer,et al.  The Power of Non-Uniform Wireless Power , 2013, SODA.

[13]  Tigran Tonoyan,et al.  Comparing Schedules in the SINR and Conflict-Graph Models with Different Power Schemes , 2013, ADHOC-NOW.

[14]  Tigran Tonoyan,et al.  On Some Bounds on the Optimum Schedule Length in the SINR Model , 2012, ALGOSENSORS.

[15]  Izhak Rubin,et al.  On the performance of graph-based scheduling algorithms for packet radio networks , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[16]  Magnús M. Halldórsson,et al.  Wireless capacity with oblivious power in general metrics , 2011, SODA '11.

[17]  Thomas Kesselheim,et al.  A constant-factor approximation for wireless capacity maximization with power control in the SINR model , 2010, SODA '11.

[18]  Aravind Srinivasan,et al.  Approximation Algorithms for Computing Capacity of Wireless Networks with SINR Constraints , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[19]  Magnús M. Halldórsson.  Locality in wireless scheduling , 2013, SPAA.

[20]  Theodore S. Rappaport,et al.  Wireless communications - principles and practice , 1996 .

[21]  Zvi Lotker,et al.  Unit disk graph and physical interference model: Putting pieces together , 2009, 2009 IEEE International Symposium on Parallel & Distributed Processing.

[22]  Thomas Erlebach,et al.  Algorithms for Sensor Systems , 2011, Lecture Notes in Computer Science.

[23]  Catherine Rosenberg,et al.  What is the right model for wireless channel interference? , 2009, IEEE Trans. Wirel. Commun..

[24]  Roger Wattenhofer,et al.  The Complexity of Connectivity in Wireless Networks , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[25]  Noga Alon.  Splitting digraphs , 2006, Comb. Probab. Comput..

[26]  Anders Hansson,et al.  Comparison between graph-based and interference-based STDMA scheduling , 2001, MobiHoc '01.