Upper Bounds on Broadcasting Time in UDG Radio Networks with Unknown Topology

The paper considers broadcasting in radio networks, modeled as unit disk graphs (UDG). Network stations are modeled as points in the plane, where a station is connected to all stations at Euclidean distance at most 1 from it. A message transmitted by a station reaches all its neighbors, but a station hears a message (receives the message correctly) only if exactly one of its neighbors transmits at a given time step. One station of the network, called the source, has a message which has to be disseminated to all other stations. Stations are unaware of the network topology. Two broadcasting models are considered. In the conditional wake up model, the stations other than the source are initially idle and cannot transmit until they hear a message for the first time. In the spontaneous wake up model, all stations are awake (and may transmit messages) from the beginning. It turns out that broadcasting time depends on two parameters of the UDG network, namely, its diameter D and its granularity g, which is the inverse of the minimum Euclidean distance between any two stations. For the conditional wake up model, we prove that any deterministic algorithm requires Ω(D √ g) time to accomplish broadcasting. This narrows the gap left by the best known broadcasting algorithm in this model which works in time O(Dg). For the spontaneous wake up model, we establish a tight lower bound of Ω ( min { D + g, D log g }) on deterministic broadcasting time. Thus our results yield a provable separation between the two models: for some parameter values, the lower bound in the first model is significantly larger than the upper bound in the second. keywords: radio network, unit disk graph, ad hoc network, algorithm, broadcasting ∗Department of Computer Science, The University of Liverpool, Ashton Building, Ashton Street, Liverpool L69 3BX, UK. E-mail:{leszek,suc}@csc.liv.ac.uk. †Département d’informatique, Université du Québec en Outaouais, Gatineau, Québec J8X 3X7, Canada. E-mail: pelc@uqo.ca. Research partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. ‡Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel. E-mail: {yuval.emek,erez.kantor,david.peleg}@weizmann.ac.il. Supported in part by grants from the Minerva Foundation and the Israel Ministry of Science.

[1]  Andrzej Pelc,et al.  Broadcasting in geometric radio networks , 2007, J. Discrete Algorithms.

[2]  Roger Wattenhofer,et al.  Coloring unstructured radio networks , 2005, SPAA '05.

[3]  Roger Wattenhofer,et al.  Maximal independent sets in radio networks , 2005, PODC '05.

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

[5]  Andrzej Pelc,et al.  Time complexity of radio broadcasting: adaptiveness vs. obliviousness and randomization vs. determinism , 2005, Theor. Comput. Sci..

[6]  Dariusz R. Kowalski,et al.  Fast Distributed Algorithm for Convergecast in Ad Hoc Geometric Radio Networks , 2005, Second Annual Conference on Wireless On-demand Network Systems and Services.

[7]  Dariusz R. Kowalski,et al.  A better wake-up in radio networks , 2004, PODC '04.

[8]  Andrzej Pelc,et al.  Time of Deterministic Broadcasting in Radio Networks with Local Knowledge , 2004, SIAM J. Comput..

[9]  Marek Chrobak,et al.  The wake-up problem in multi-hop radio networks , 2004, SODA '04.

[10]  Wojciech Rytter,et al.  Broadcasting algorithms in radio networks with unknown topology , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

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

[12]  Andrea E. F. Clementi,et al.  Distributed broadcast in radio networks of unknown topology , 2003, Theor. Comput. Sci..

[13]  Tomasz Jurdzinski,et al.  Probabilistic Algorithms for the Wakeup Problem in Single-Hop Radio Networks , 2002, ISAAC.

[14]  Andrzej Pelc,et al.  Fault-Tolerant Broadcasting in Radio Networks , 2001, J. Algorithms.

[15]  Andrea E. F. Clementi,et al.  Selective families, superimposed codes, and broadcasting on unknown radio networks , 2001, SODA '01.

[16]  Andrzej Pelc,et al.  The Wakeup Problem in Synchronous Broadcast Systems , 2000, SIAM J. Discret. Math..

[17]  Wojciech Rytter,et al.  Fast broadcasting and gossiping in radio networks , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[18]  Anna Pagh,et al.  Deterministic Radio Broadcasting , 2000, ICALP.

[19]  Wojciech Rytter,et al.  Deterministic broadcasting in unknown radio networks , 2000, SODA '00.

[20]  Danilo Bruschi,et al.  Lower bounds for the broadcast problem in mobile radio networks , 1997, Distributed Computing.

[21]  Arunabha Sen,et al.  A new model for scheduling packet radio networks , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[22]  Suresh Singh,et al.  Broadcasting on [0, L] , 1994, Discret. Appl. Math..

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

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

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

[26]  Reuven Bar-Yehuda,et al.  On the time-complexity of broadcast in radio networks: an exponential gap between determinism randomization , 1987, PODC '87.

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

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

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