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On the effect of the deployment setting on broadcasting in Euclidean radio networks

Published: 18 August 2008 Publication History

Abstract

The paper studies broadcasting in radio networks whose stations are represented by points in the Euclidean plane. In any given time step, a station can either receive or transmit. A message transmitted from station (v) is delivered to every station (u) at distance at most (1) from (v), but (u) successfully hears the message if and only if (v) is the only station at distance at most (1) from (u) that transmitted in this time step. A designated source station has a message that should be disseminated throughout the network. All stations other than the source are initially idle and wake up upon the first time they hear the source message.
It is shown in [11] that the time complexity of broadcasting depends on two parameters of the network, namely, its diameter (in hops) (D) and a lower bound (d) on the Euclidean distance between any two stations. The inverse of (d) is called the granularity of the network, denoted by (g). Specifically, the authors of [11] present a broadcasting algorithm that works in time (O (D g)) and prove that every broadcasting algorithm requires Ω (D √g) time. In this paper, we distinguish between the arbitrary deployment setting, originally studied in [11], in which stations can be placed everywhere in the plane, and the new grid deployment setting, in which stations are only allowed to be placed on a (d)-spaced grid. Does the latter (more restricted) setting provides any speedup in broadcasting time complexity? Although the (O (D g)) broadcasting algorithm of [11] works under the (original) arbitrary deployment setting, it turns out that the Ω (D √g) lower bound remains valid under the grid deployment setting. Still, the above question is left unanswered. The current paper answers this question affirmatively by presenting a provable separation between the two deployment settings. We establish a tight lower bound on the time complexity of broadcasting under the arbitrary deployment setting proving that broadcasting cannot be completed in less than Ω ( D √g) time. For the grid deployment setting, we develop a broadcasting algorithm that runs in time O ( D g5 / 6 log g), thus breaking the linear dependency on (g).

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cover image ACM Conferences
PODC '08: Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
August 2008
474 pages
ISBN:9781595939890
DOI:10.1145/1400751
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 18 August 2008

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Author Tags

  1. ad hoc networks
  2. broadcasting
  3. radio networks
  4. unit disk graphs

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  • (2013)Message and time efficient multi-broadcast schemesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.132.3132(21-37)Online publication date: 17-Oct-2013
  • (2013)Fast message dissemination in random geometric networksDistributed Computing10.1007/s00446-011-0154-426:1(1-24)Online publication date: 1-Feb-2013
  • (2013)Distributed Randomized Broadcasting in Wireless Networks under the SINR ModelProceedings of the 27th International Symposium on Distributed Computing - Volume 820510.1007/978-3-642-41527-2_26(373-387)Online publication date: 14-Oct-2013
  • (2013)Distributed deterministic broadcasting in wireless networks of weak devicesProceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II10.1007/978-3-642-39212-2_55(632-644)Online publication date: 8-Jul-2013
  • (2011)Synchronous rendezvous for location-aware agentsProceedings of the 25th international conference on Distributed computing10.5555/2075029.2075084(447-459)Online publication date: 20-Sep-2011
  • (2011)Interference-aware broadcast scheduling in wireless networksAd Hoc Networks10.1016/j.adhoc.2010.12.0029:7(1069-1082)Online publication date: 1-Sep-2011
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