A Local Broadcast Layer for the SINR Network Model

We present the first algorithm that implements an abstract MAC (absMAC) layer in the Signal-to-Interference-plus-Noise-Ratio (SINR) wireless network model. We first prove that efficient SINR implementations are not possible for the standard absMAC specification. We modify that specification to an "approximate" version that better suits the SINR model. We give an efficient algorithm to implement the modified specification, and use it to derive efficient algorithms for higher-level problems of global broadcast and consensus. In particular, we show that the absMAC progress property has no efficient implementation in terms of the SINR strong connectivity graph G1-ε, which contains edges between nodes of distance at most (1-ε) times the transmission range, where ε>0 is a small constant that can be chosen by the user. This progress property bounds the time until a node is guaranteed to receive some message when at least one of its neighbors is transmitting. To overcome this limitation, we introduce the slightly weaker notion of approximate progress into the absMAC specification. We provide a fast implementation of the modified specification, based on decomposing the algorithm of [10] into local and global parts. We analyze our algorithm in terms of local parameters such as node degrees, rather than global parameters such as the overall number of nodes. A key contribution is our demonstration that such a local analysis is possible even in the presence of global interference. Our absMAC algorithm leads to several new, efficient algorithms for solving higher-level problems in the SINR model. Namely, by combining our algorithm with high-level algorithms from [26], we obtain an improved (compared to [10]) algorithm for global single-message broadcast in the SINR model, and the first efficient algorithm for multi-message broadcast in that model. We also derive the first efficient algorithm for network-wide consensus, using a result of [32]. This work demonstrates that one can develop efficient algorithms for solving high-level problems in the SINR model, using graph-based algorithms over a local broadcast abstraction layer that hides the technicalities of the SINR platform such as global interference. Our algorithms do not require bounds on the network size, nor the ability to measure signal strength, nor carrier sensing, nor synchronous wakeup.

[1]  Paul D. Ezhilchelvan,et al.  Consensus in Sparse, Mobile Ad Hoc Networks , 2012, IEEE Transactions on Parallel and Distributed Systems.

[2]  Francis C. M. Lau,et al.  An O(log n) Distributed Approximation Algorithm for Local Broadcasting in Unstructured Wireless Networks , 2012, 2012 IEEE 8th International Conference on Distributed Computing in Sensor Systems.

[3]  Eyal Kushilevitz,et al.  An Omega(D log (N/D)) Lower Bound for Broadcast in Radio Networks , 1998, SIAM J. Comput..

[4]  Roger Wattenhofer,et al.  Local broadcasting in the physical interference model , 2008, DIALM-POMC '08.

[5]  Yishay Mansour,et al.  Centralized broadcast in multihop radio networks , 2003, J. Algorithms.

[6]  Calvin C. Newport,et al.  Broadcast in the Ad Hoc SINR Model , 2013, DISC.

[7]  Nancy A. Lynch,et al.  Multi-message broadcast with abstract MAC layers and unreliable links , 2014, PODC '14.

[8]  Nancy A. Lynch,et al.  Bounds on Contention Management in Radio Networks , 2012, DISC.

[9]  Jennifer L. Welch,et al.  Reliable neighbor discovery for mobile ad hoc networks , 2010, DIALM-POMC '10.

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

[11]  Christian Scheideler,et al.  An O(log n) dominating set protocol for wireless ad-hoc networks under the physical interference model , 2008, MobiHoc '08.

[12]  Nancy A. Lynch,et al.  Decomposing broadcast algorithms using abstract MAC layers , 2010, DIALM-POMC '10.

[13]  Reuven Bar-Yehuda,et al.  On the Time-Complexity of Broadcast in Multi-hop Radio Networks: An Exponential Gap Between Determinism and Randomization , 1992, J. Comput. Syst. Sci..

[14]  Magnús M. Halldórsson,et al.  Nearly optimal bounds for distributed wireless scheduling in the SINR model , 2011, Distributed Computing.

[15]  David Peleg,et al.  Faster communication in known topology radio networks , 2005, PODC '05.

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

[17]  Guy Kortsarz,et al.  Improved schedule for radio broadcast , 2005, SODA '05.

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

[19]  David Peleg,et al.  Time-Efficient Broadcasting in Radio Networks: A Review , 2007, ICDCIT.

[20]  Majid Khabbazian,et al.  Time-efficient randomized multiple-message broadcast in radio networks , 2011, PODC '11.

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

[22]  Majid Khabbazian,et al.  A Bound on the Throughput of Radio Networks , 2013, ArXiv.

[23]  Andrzej Pelc,et al.  Broadcasting in undirected ad hoc radio networks , 2003, PODC '03.

[24]  Calvin C. Newport.  Consensus with an abstract MAC layer , 2014, PODC '14.

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

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

[27]  Roger Wattenhofer,et al.  A log-star distributed maximal independent set algorithm for growth-bounded graphs , 2008, PODC '08.

[28]  Imrich Chlamtac,et al.  On Broadcasting in Radio Networks - Problem Analysis and Protocol Design , 1985, IEEE Transactions on Communications.

[29]  Dariusz R. Kowalski,et al.  Distributed Deterministic Broadcasting in Wireless Networks of Weak Devices , 2012, ICALP.

[30]  Francis C. M. Lau,et al.  Distributed multiple-message broadcast in wireless ad hoc networks under the SINR model , 2016, Theor. Comput. Sci..

[31]  Eyal Kushilevitz,et al.  An Ω(D log(N/D)) lower bound for broadcast in radio networks , 1993, PODC '93.

[32]  Murat Demirbas,et al.  Consensus and collision detectors in wireless Ad Hoc networks , 2005, PODC '05.

[33]  Noga Alon,et al.  A Lower Bound for Radio Broadcast , 1991, J. Comput. Syst. Sci..

[34]  Imrich Chlamtac,et al.  The wave expansion approach to broadcasting in multihop radio networks , 1991, IEEE Trans. Commun..

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

[36]  Dariusz R. Kowalski,et al.  Distributed Randomized Broadcasting in Wireless Networks under the SINR Model , 2013, Encyclopedia of Algorithms.

[37]  Nancy A. Lynch,et al.  The abstract MAC layer , 2009, Distributed Computing.

[38]  Andrzej Pelc,et al.  Optimal Deterministic Broadcasting in Known Topology Radio Networks , 2006, Distributed Computing.

[39]  Jennifer L. Welch,et al.  Neighbor discovery in mobile ad hoc networks using an abstract MAC layer , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[40]  Magnús M. Halldórsson,et al.  Towards tight bounds for local broadcasting , 2012, FOMC '12.

[41]  Francis C. M. Lau,et al.  Deterministic Distributed Data Aggregation under the SINR Model , 2012, TAMC.

[42]  Nancy A. Lynch,et al.  MAC design for analog network coding , 2011, FOMC '11.

[43]  Wojciech Rytter,et al.  Broadcasting algorithms in radio networks with unknown topology , 2006, J. Algorithms.

[44]  Dariusz R. Kowalski,et al.  On the impact of geometry on ad hoc communication in wireless networks , 2014, PODC '14.

[45]  Reuven Bar-Yehuda,et al.  Multiple Communication in Multihop Radio Networks , 1993, SIAM J. Comput..

[46]  Jiguo Yu,et al.  Efficient distributed multiple-message broadcasting in unstructured wireless networks , 2013, 2013 Proceedings IEEE INFOCOM.

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

[48]  Moti Medina,et al.  Multi-Hop Routing and Scheduling in Wireless Networks in the SINR model , 2011, ALGOSENSORS.

[49]  Majid Khabbazian,et al.  Randomized broadcast in radio networks with collision detection , 2013, PODC '13.