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Efficient Broadcasting in Known Geometric Radio Networks with Non-uniform Ranges

Gasieniec, Leszek; Kowalski, Dariusz; Lingas, Andrzej LU and Wahlén, Martin LU (2008) International Symposium on Distributed Computing (DISC) In Lecture Notes in Computer Science/Proceedings of the 22nd International Symposium on Distributed Computing 5218. p.274-288
Abstract
We study here deterministic broadcasting in geometric radio networks (GRN) whose nodes have complete knowledge of the network. Nodes of a GRN are deployed in the Euclidean plane (R 2) and each of them can transmit within some range r assigned to it. We adopt model in which ranges of nodes are non-uniform and they are drawn from the predefined interval 0 ≤ r min  ≤ r max . All our results are in the conflict-embodied model where a receiving node must be in the range of exactly one transmitting node in order to receive the message.

We derive several lower and upper bounds on the time of deterministic broadcasting in GRNs in terms of the number of nodes n, a distribution of nodes ranges, and the eccentricity D of the source node... (More)
We study here deterministic broadcasting in geometric radio networks (GRN) whose nodes have complete knowledge of the network. Nodes of a GRN are deployed in the Euclidean plane (R 2) and each of them can transmit within some range r assigned to it. We adopt model in which ranges of nodes are non-uniform and they are drawn from the predefined interval 0 ≤ r min  ≤ r max . All our results are in the conflict-embodied model where a receiving node must be in the range of exactly one transmitting node in order to receive the message.

We derive several lower and upper bounds on the time of deterministic broadcasting in GRNs in terms of the number of nodes n, a distribution of nodes ranges, and the eccentricity D of the source node (i.e., the maximum length of a shortest directed path from the source node to another node in the network). In particular:

(1) We show that D + Ω(log(n − D)) rounds are required to accomplish broadcasting in some GRN where each node has the transmission range set either to 1 or to 0. We also prove that the bound D + Ω(log(n − D)) is almost tight providing a broadcasting procedure that works in this type of GRN in time D + O(logn).

(2) In GRNs with a wider choice of positive node ranges from r min , ...,r max , we show that broadcasting requires rounds and that it can be accomplished in rounds subsuming the best currently known upper bound provided in [15].

(3) We also study the problem of simulation of minimum energy broadcasting in arbitrary GRNs. We show that energy optimal broadcasting that can be completed in h rounds in a conflict-free model may require up to h/2 additional rounds in the conflict-embodied model. This lower bound should be seen as a separation result between conflict-free and conflict-embodied geometric radio networks. Finally, we also prove that any h-hop broadcasting algorithm with the energy consumption in a GRN can be simulated within O(hlogψ) rounds in the conflict-embodied model using energy O(cal E), where ψ is the ratio between the largest and the shortest Euclidean distance between a pair of nodes in the network. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Lecture Notes in Computer Science/Proceedings of the 22nd International Symposium on Distributed Computing
editor
Taubenfeld, Gadi and
volume
5218
pages
274 - 288
publisher
Springer
conference name
International Symposium on Distributed Computing (DISC)
external identifiers
  • scopus:56449096257
ISSN
1611-3349
0302-9743
ISBN
978-3-540-87778-3
DOI
10.1007/978-3-540-87779-0_19
project
VR 2005-4085
language
English
LU publication?
yes
id
fe01d91f-4025-4277-8548-4eba5f9fb40e (old id 1288735)
date added to LUP
2009-02-03 10:17:17
date last changed
2017-03-05 03:39:19
@inproceedings{fe01d91f-4025-4277-8548-4eba5f9fb40e,
  abstract     = {We study here deterministic broadcasting in geometric radio networks (GRN) whose nodes have complete knowledge of the network. Nodes of a GRN are deployed in the Euclidean plane (R 2) and each of them can transmit within some range r assigned to it. We adopt model in which ranges of nodes are non-uniform and they are drawn from the predefined interval 0 ≤ r min  ≤ r max . All our results are in the conflict-embodied model where a receiving node must be in the range of exactly one transmitting node in order to receive the message.<br/><br>
We derive several lower and upper bounds on the time of deterministic broadcasting in GRNs in terms of the number of nodes n, a distribution of nodes ranges, and the eccentricity D of the source node (i.e., the maximum length of a shortest directed path from the source node to another node in the network). In particular:<br/><br>
(1) We show that D + Ω(log(n − D)) rounds are required to accomplish broadcasting in some GRN where each node has the transmission range set either to 1 or to 0. We also prove that the bound D + Ω(log(n − D)) is almost tight providing a broadcasting procedure that works in this type of GRN in time D + O(logn).<br/><br>
(2) In GRNs with a wider choice of positive node ranges from r min , ...,r max , we show that broadcasting requires rounds and that it can be accomplished in rounds subsuming the best currently known upper bound provided in [15].<br/><br>
(3) We also study the problem of simulation of minimum energy broadcasting in arbitrary GRNs. We show that energy optimal broadcasting that can be completed in h rounds in a conflict-free model may require up to h/2 additional rounds in the conflict-embodied model. This lower bound should be seen as a separation result between conflict-free and conflict-embodied geometric radio networks. Finally, we also prove that any h-hop broadcasting algorithm with the energy consumption in a GRN can be simulated within O(hlogψ) rounds in the conflict-embodied model using energy O(cal E), where ψ is the ratio between the largest and the shortest Euclidean distance between a pair of nodes in the network.},
  author       = {Gasieniec, Leszek and Kowalski, Dariusz and Lingas, Andrzej and Wahlén, Martin},
  booktitle    = {Lecture Notes in Computer Science/Proceedings of the 22nd International Symposium on Distributed Computing},
  editor       = {Taubenfeld, Gadi},
  isbn         = {978-3-540-87778-3},
  issn         = {1611-3349},
  language     = {eng},
  pages        = {274--288},
  publisher    = {Springer},
  title        = {Efficient Broadcasting in Known Geometric Radio Networks with Non-uniform Ranges},
  url          = {http://dx.doi.org/10.1007/978-3-540-87779-0_19},
  volume       = {5218},
  year         = {2008},
}