arXiv subjects

Peter Davies

Publications and source records attributed to Peter Davies.

22 records · Page 2Linked to original sources

arXiv2019

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, based on the existence of small universal synchronizers. This algorithm runs in $O(\frac{\min\{n, D Δ\} \log n \log Δ}{\log\log Δ})$ time, the fastest known in both directed and undirected networks, improving over the previous best $O(n \log^2n)$-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 $O(n \log D \log\log\frac{D Δ}{n})$ time. This is the fastest known algorithm for the problem in directed networks, 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). It is also the first to come within a log-logarithmic factor of the $Ω(n \log D)$ 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.

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arXiv2018

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 \emph{deterministic} algorithms for \emph{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). Specifically, in multiple access channels with $k$ participating nodes and IDs up to $L$, we give a wake-up algorithm requiring $O(\frac{k\log L \log k }{\log\log k})$ time, improving dramatically over the $O(L^3 \log^3 L)$ time algorithm of De Marco et al. (2007), and a broadcasting algorithm requiring \sloppy{$O(k\log L \log\log k)$ }time, improving over the $O(L)$ time algorithm of Gasieniec et al. (2001) in most circumstances. Furthermore, we show how these same algorithms apply directly to multi-hop radio networks, achieving even larger running time improvements.

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arXiv2018

Randomized Communication Without Network Knowledge

Radio networks are a long-studied model for distributed system of devices which communicate wirelessly. When these devices are mobile or have limited capabilities, the system is often best modeled by the ad-hoc variant, in which the devices do not know the structure of the network. A large body of work has been devoted to designing algorithms for the ad-hoc model, particularly for fundamental communications tasks such as broadcasting. Most of these algorithms, however, assume that devices have some network knowledge (usually bounds on the number of nodes in the network $n$, and the diameter $D$), which may not always be realistic in systems with weak devices or gradual deployment. Very little is known about what can be done when this information is not available. This is the issue we address in this work, by presenting the first \emph{randomized} broadcasting algorithms for \emph{blind} networks in which nodes have no prior knowledge whatsoever. We demonstrate that lack of parameter knowledge can be overcome at only a small increase in running time. Specifically, we show that in networks without collision detection, broadcast can be achieved in $O(D\log\frac nD\log^2\log\frac nD + \log^2 n)$ time, almost reaching the $Ω(D\log\frac nD + \log^2 n)$ lower bound. We also give an algorithm for directed networks with collision detection, which requires only $O(D\log\frac nD\log\log\log\frac nD + \log^2 n)$ time.

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arXiv2017

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 Omega(D log n/D + log^2 n) rounds in expectation, 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 slightly improved for the model with spontaneous transmissions, providing an O(D log n loglog n / log D + log^O(1) n)-time broadcasting algorithm. In this paper, we give a new and faster algorithm that completes broadcasting in O(D log n/log D + log^O(1) n) time, with high probability. This yields the first optimal O(D)-time broadcasting algorithm whenever D is polynomial in n. 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 been using broadcasting as their subroutine and their complexity have been asymptotically strictly bigger 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{loglog n, log n/D} + log^O(1) n)-time with high probability. Our new algorithm requires O(D log n / log D + log^O(1) n) time with high probability, and it achieves the optimal O(D) time whenever D is polynomial in n.

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