23 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
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 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
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
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
On Permutation Selectors and their Applications in Ad-Hoc Radio Networks Protocols
Selective families of sets, or selectors, are combinatorial tools used to
"isolate" individual members of sets from some set family. Given a set and
an element , to isolate from , at least one of the sets in the
selector must intersect on exactly . We study (k,N)-permutation
selectors which have the property that they can isolate each element of each
-element subset of in each possible order. These selectors
can be used in protocols for ad-hoc radio networks to more efficiently
disseminate information along multiple hops. In 2004, Gasieniec, Radzik and Xin
gave a construction of a (k,N)-permutation selector of size .
This paper improves this by providing a probabilistic construction of a
(k,N)-permutation selector of size . Remarkably, this matches the
asymptotic bound for standard strong (k,N)-selectors, that isolate each element
of each set of size , but with no restriction on the order. We then show
that the use of our (k,N)-permutation selector improves the best running time
for gossiping in ad-hoc radio networks by a poly-logarithmic factor.Comment: 9 pages, 2 figure
Deterministic blind radio networks
Ad-hoc radio networks and multiple access channels are classical and well-studied models of distributed systems, with a large body of literature on deterministic algorithms for fundamental communications primitives such as broadcasting and wake-up. However, almost all of these algorithms assume knowledge of the number of participating nodes and the range of possible IDs, and often make the further assumption that the latter is linear in the former. These are very strong assumptions for models which were designed to capture networks of weak devices organized in an ad-hoc manner. It was believed that without this knowledge, deterministic algorithms must necessarily be much less efficient.
In this paper we address this fundamental question and show that this is not the case. We present deterministic algorithms for blind networks (in which nodes know only their own IDs), which match or nearly match the running times of the fastest algorithms which assume network knowledge (and even surpass the previous fastest algorithms which assume parameter knowledge but not small labels)