5,298 research outputs found
Deterministic Communication in Radio Networks
In this paper we improve the deterministic complexity of two fundamental
communication primitives in the classical model of ad-hoc radio networks with
unknown topology: broadcasting and wake-up. We consider an unknown radio
network, in which all nodes have no prior knowledge about network topology, and
know only the size of the network , the maximum in-degree of any node
, and the eccentricity of the network .
For such networks, we first give an algorithm for wake-up, based on the
existence of small universal synchronizers. This algorithm runs in
time, the
fastest known in both directed and undirected networks, improving over the
previous best -time result across all ranges of parameters, but
particularly when maximum in-degree is small.
Next, we introduce a new combinatorial framework of block synchronizers and
prove the existence of such objects of low size. Using this framework, we
design a new deterministic algorithm for the fundamental problem of
broadcasting, running in time. This is
the fastest known algorithm for the problem in directed networks, improving
upon the -time algorithm of De Marco (2010) and the
-time algorithm due to Czumaj and Rytter (2003). It is also the
first to come within a log-logarithmic factor of the lower
bound due to Clementi et al.\ (2003).
Our results also have direct implications on the fastest \emph{deterministic
leader election} and \emph{clock synchronization} algorithms in both directed
and undirected radio networks, tasks which are commonly used as building blocks
for more complex procedures
Exploiting spontaneous transmissions for broadcasting and leader election in radio networks
We study two fundamental communication primitives: broadcasting and leader election in the classical model of multi-hop radio networks with unknown topology and without collision detection mechanisms. It has been known for almost 20 years that in undirected networks with n nodes and diameter D, randomized broadcasting requires Ω(D log n/D + log2 n) rounds, assuming that uninformed nodes are not allowed to communicate (until they are informed). Only very recently, Haeupler and Wajc (PODC'2016) showed that this bound can be improved for the model with spontaneous transmissions, providing an O(D log n log log n/log D + logO(1) n)-time broadcasting algorithm. In this article, we give a new and faster algorithm that completes broadcasting in O(D log n/log D + logO(1) n) time, succeeding with high probability. This yields the first optimal O(D)-time broadcasting algorithm whenever n is polynomial in D.
Furthermore, our approach can be applied to design a new leader election algorithm that matches the performance of our broadcasting algorithm. Previously, all fast randomized leader election algorithms have used broadcasting as a subroutine and their complexity has been asymptotically strictly larger than the complexity of broadcasting. In particular, the fastest previously known randomized leader election algorithm of Ghaffari and Haeupler (SODA'2013) requires O(D log n/D min {log log n, log n/D} + logO(1) n)-time, succeeding with high probability. Our new algorithm again requires O(D log n/log D + logO(1) n) time, also succeeding with high probability
Faster deterministic communication in radio networks
In this paper we improve the deterministic complexity of two fundamental communication primitives in the classical model of ad-hoc radio networks with unknown topology: broadcasting and wake-up. We consider an unknown radio network, in which all nodes have no prior knowledge about network topology, and know only the size of the network n, the maximum in-degree of any node Δ, and the eccentricity of the network D.
For such networks, we first give an algorithm for wake-up, in both directed and undirected networks, based on the existence of small universal synchronizers. This algorithm runs in O(min{n,DΔ}lognlogΔloglogΔ) time, improving over the previous best O(nlog2n)-time result across all ranges of parameters, but particularly when maximum in-degree is small.
Next, we introduce a new combinatorial framework of block synchronizers and prove the existence of such objects of low size. Using this framework, we design a new deterministic algorithm for the fundamental problem of broadcasting, running in O(nlogDloglogDΔn) time. This is the fastest known algorithm for this problems, improving upon the O(nlognloglogn)-time algorithm of De Marco (2010) and the O(nlog2D)-time algorithm due to Czumaj and Rytter (2003), the previous fastest results for directed networks, and is the first to come within a log-logarithmic factor of the Ω(nlogD) lower bound due to Clementi et al. (2003).
Our results have also direct implications on the fastest deterministic leader election and clock synchronization algorithms in both directed and undirected radio networks, tasks which are commonly used as building blocks for more complex procedures
Faster Gossiping in Bidirectional Radio Networks with Large Labels
We consider unknown ad-hoc radio networks, when the underlying network is
bidirectional and nodes can have polynomially large labels. For this model, we
present a deterministic protocol for gossiping which takes rounds. This improves upon the previous best result for deterministic
gossiping for this model by [Gasienec, Potapov, Pagourtizis, Deterministic
Gossiping in Radio Networks with Large labels, ESA (2002)], who present a
protocol of round complexity for this problem. This
resolves open problem posed in [Gasienec, Efficient gossiping in radio
networks, SIROCCO (2009)], who cite bridging gap between lower and upper bounds
for this problem as an important objective. We emphasize that a salient feature
of our protocol is its simplicity, especially with respect to the previous best
known protocol for this problem
Faster Deterministic Communication in Radio Networks
In this paper we improve the deterministic complexity of two fundamental communication primitives in the classical model of ad-hoc radio networks with unknown topology: broadcasting and wake-up. We consider an unknown radio network, in which all nodes have no prior knowledge about network topology, and know only the size of the network n, the maximum in-degree of any node Delta, and the eccentricity of the network D.
For such networks, we first give an algorithm for wake-up, in both directed and undirected networks, based on the existence of small universal synchronizers. This algorithm runs in O((min{n,D*Delta}*log(n)*log(Delta))/(log(log(Delta)))) time, improving over the previous best O(n*log^2(n))-time result across all ranges of parameters, but particularly when maximum in-degree is small.
Next, we introduce a new combinatorial framework of block synchronizers and prove the existence of such objects of low size. Using this framework, we design a new deterministic algorithm for the fundamental problem of broadcasting, running in O(n*log(D)*log(log((D*Delta)/n))) time. This is the fastest known algorithm for this problems, improving upon the O(n*log(n)*log*log(n))-time algorithm of De Marco (2010) and the O(n*log^2(D))-time algorithm due to Czumaj and Rytter (2003), the previous fastest results for directed networks, and is the first to come within a log-logarithmic factor of the Omega(n*log(D)) lower bound due to Clementi et al. (2003).
Our results have also direct implications on the fastest deterministic leader election and clock synchronization algorithms in both directed and undirected radio networks, tasks which are commonly used as building blocks for more complex procedures
Message and time efficient multi-broadcast schemes
We consider message and time efficient broadcasting and multi-broadcasting in
wireless ad-hoc networks, where a subset of nodes, each with a unique rumor,
wish to broadcast their rumors to all destinations while minimizing the total
number of transmissions and total time until all rumors arrive to their
destination. Under centralized settings, we introduce a novel approximation
algorithm that provides almost optimal results with respect to the number of
transmissions and total time, separately. Later on, we show how to efficiently
implement this algorithm under distributed settings, where the nodes have only
local information about their surroundings. In addition, we show multiple
approximation techniques based on the network collision detection capabilities
and explain how to calibrate the algorithms' parameters to produce optimal
results for time and messages.Comment: In Proceedings FOMC 2013, arXiv:1310.459
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