Arbitrary Throughput Versus Complexity Tradeoffs in Wireless Networks Using Graph Partitioning

Several policies have recently been proposed for attaining the maximum throughput region, or a guaranteed fraction thereof, through dynamic link scheduling. Among these policies, the ones that attain the maximum throughput region require a computation time which is linear in the network size, and the ones that require constant or logarithmic computation time attain only certain fractions of the maximum throughput region. In contrast, in this paper we propose policies that can attain any desirable fraction of the maximum throughput region using a computation time that is largely independent of the network size. First, using a combination of graph partitioning techniques and Lyapunov arguments, we propose a simple policy for tree topologies under the primary interference model that requires each link to exchange only 1 bit information with its adjacent links and approximates the maximum throughput region using a computation time that depends only on the maximum degree of nodes and the approximation factor. Then we develop a framework for attaining arbitrary close approximations for the maximum throughput region in arbitrary networks, and use this framework to obtain any desired tradeoff between throughput guarantees and computation times for a large class of networks and interference models. Specifically, given any epsiv > 0, the maximum throughput region can be approximated in these networks within a factor of 1-epsiv using a computation time that depends only on the maximum node degree and epsiv .

[1]  Harry B. Hunt,et al.  NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs , 1998, J. Algorithms.

[2]  Leandros Tassiulas,et al.  Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks , 1992 .

[3]  Leandros Tassiulas,et al.  Distributed dynamic scheduling for end-to-end rate guarantees in wireless ad hoc networks , 2005, MobiHoc '05.

[4]  Kyomin Jung,et al.  Low Delay Scheduling in Wireless Network , 2007, 2007 IEEE International Symposium on Information Theory.

[5]  Alon Itai,et al.  A Fast and Simple Randomized Parallel Algorithm for Maximal Matching , 1986, Inf. Process. Lett..

[6]  Eytan Modiano,et al.  Maximizing throughput in wireless networks via gossiping , 2006, SIGMETRICS '06/Performance '06.

[7]  Bruce E. Hajek,et al.  Link scheduling in polynomial time , 1988, IEEE Trans. Inf. Theory.

[8]  R. Srikant,et al.  Distributed Link Scheduling With Constant Overhead , 2006, IEEE/ACM Transactions on Networking.

[9]  Xiaojun Lin,et al.  Constant-Time Distributed Scheduling Policies for Ad Hoc Wireless Networks , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[10]  Xiaojun Lin,et al.  The Impact of Imperfect Scheduling on Cross-Layer Rate Control in Multihop Wireless Networks , 2022 .

[11]  Leandros Tassiulas.  Scheduling and performance limits of networks with constantly changing topology , 1997 .

[12]  Ness B. Shroff,et al.  On the Complexity of Scheduling in Wireless Networks , 2006, MobiCom '06.

[13]  Eytan Modiano,et al.  Fairness and optimal stochastic control for heterogeneous networks , 2005, INFOCOM.

[14]  Jennifer C. Hou,et al.  Topology control in heterogeneous wireless networks: problems and solutions , 2004, IEEE INFOCOM 2004.

[15]  Prasanna Chaporkar,et al.  Throughput Guarantees Through Maximal Scheduling in Wireless Networks , 2008 .

[16]  J. Walrand,et al.  Sufficient conditions for stability of longest-queue-first scheduling: second-order properties using fluid limits , 2006, Advances in Applied Probability.

[17]  Eytan Modiano,et al.  Enabling distributed throughput maximization in wireless mesh networks: a partitioning approach , 2006, MobiCom '06.

[18]  Koushik Kar,et al.  Achieving 2 / 3 Throughput Approximation with Sequential Maximal Scheduling under Primary Interference Constraints , 2006 .

[19]  E. Modiano,et al.  Distributed Throughput Maximization in Wireless Mesh Networks via Pre-Partitioning , 2008, IEEE/ACM Transactions on Networking.

[20]  G. Fayolle,et al.  Topics in the Constructive Theory of Countable Markov Chains , 1995 .

[21]  Michael Luby,et al.  A simple parallel algorithm for the maximal independent set problem , 1985, STOC '85.

[22]  Balaji Prabhakar,et al.  The throughput of data switches with and without speedup , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

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

[24]  Johann Hurink,et al.  A Robust PTAS for Maximum Weight Independent Sets in Unit Disk Graphs , 2004, WG.

[25]  Roger Wattenhofer,et al.  Local approximation schemes for ad hoc and sensor networks , 2005, DIALM-POMC '05.

[26]  Leandros Tassiulas,et al.  Linear complexity algorithms for maximum throughput in radio networks and input queued switches , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[27]  Ness B. Shroff,et al.  The impact of imperfect scheduling on cross-layer rate control in wireless networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[28]  David Peleg,et al.  Distributed Computing: A Locality-Sensitive Approach , 1987 .

[29]  R. Srikant,et al.  Regulated Maximal Matching: A Distributed Scheduling Algorithm for Multi-Hop Wireless Networks With Node-Exclusive Spectrum Sharing , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[30]  Sean P. Meyn,et al.  Stability of queueing networks and scheduling policies , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.