Nearly optimal bounds for distributed wireless scheduling in the SINR model

We study the wireless scheduling problem in the SINR model. More specifically, given a set of $$n$$n links, each a sender–receiver pair, we wish to partition (or schedule) the links into the minimum number of slots, each satisfying interference constraints allowing simultaneous transmission. In the basic problem, all senders transmit with the same uniform power. We analyze a randomized distributed scheduling algorithm proposed by Kesselheim and Vöcking, and show that it achieves $$O(\log n)$$O(logn)-approximation, an improvement of a logarithmic factor. This matches the best ratio known for centralized algorithms and holds in arbitrary metric space and for every length-monotone and sublinear power assignment. We also show that every distributed algorithm uses $$\varOmega (\log n)$$Ω(logn) slots to schedule certain instances that require only two slots, which implies that the best possible absolute performance guarantee is logarithmic.

[1]  Magnús M. Halldórsson,et al.  Wireless capacity and admission control in cognitive radio , 2012, 2012 Proceedings IEEE INFOCOM.

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

[3]  Panganamala Ramana Kumar,et al.  RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN , 2001 .

[4]  Samir Ranjan Das,et al.  A measurement study of interference modeling and scheduling in low-power wireless networks , 2008, SenSys '08.

[5]  Andrea Goldsmith,et al.  Wireless Communications , 2005, 2021 15th International Conference on Advanced Technologies, Systems and Services in Telecommunications (TELSIKS).

[6]  Roger Wattenhofer,et al.  Algorithms for Wireless Capacity , 2014, IEEE/ACM Transactions on Networking.

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

[8]  Thomas Kesselheim,et al.  Approximation algorithms for spectrum allocation and power control in wireless networks , 2012 .

[9]  Roger Wattenhofer,et al.  Complexity in geometric SINR , 2007, MobiHoc '07.

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

[11]  Alessandro Panconesi,et al.  Concentration of Measure for the Analysis of Randomized Algorithms , 2009 .

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

[13]  Michael Dinitz,et al.  Distributed Algorithms for Approximating Wireless Network Capacity , 2010, 2010 Proceedings IEEE INFOCOM.

[14]  Magnús M. Halldórsson,et al.  Distributed connectivity of wireless networks , 2012, PODC '12.

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

[16]  Aravind Srinivasan,et al.  Cross-layer latency minimization in wireless networks with SINR constraints , 2007, MobiHoc '07.

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

[18]  Magnús M. Halldórsson,et al.  Connectivity and aggregation in multihop wireless networks , 2013, PODC '13.

[19]  Michael Dinitz,et al.  Maximizing Capacity in Arbitrary Wireless Networks in the SINR Model: Complexity and Game Theory , 2009, IEEE INFOCOM 2009.

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

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

[22]  Berthold Vöcking,et al.  Improved algorithms for latency minimization in wireless networks , 2009, Theor. Comput. Sci..

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

[24]  Giuseppe Di Battista,et al.  26 Computer Networks , 2004 .

[25]  Tigran Tonoyan.  On the Problem of Wireless Scheduling with Linear Power Levels , 2011, ArXiv.

[26]  Roger Wattenhofer,et al.  Capacity of Arbitrary Wireless Networks , 2009, IEEE INFOCOM 2009.

[27]  Eyjólfur Ingi Ásgeirsson,et al.  On a game theoretic approach to capacity maximization in wireless networks , 2011, 2011 Proceedings IEEE INFOCOM.

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