29 research outputs found
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On the Computational Power of Radio Channels
Radio networks can be a challenging platform for which to develop distributed algorithms, because the network nodes must contend for a shared channel. In some cases, though, the shared medium is an advantage rather than a disadvantage: for example, many radio network algorithms cleverly use the shared channel to approximate the degree of a node, or estimate the contention. In this paper we ask how far the inherent power of a shared radio channel goes, and whether it can efficiently compute "classicaly hard" functions such as Majority, Approximate Sum, and Parity.
Using techniques from circuit complexity, we show that in many cases, the answer is "no". We show that simple radio channels, such as the beeping model or the channel with collision-detection, can be approximated by a low-degree polynomial, which makes them subject to known lower bounds on functions such as Parity and Majority; we obtain round lower bounds of the form Omega(n^{delta}) on these functions, for delta in (0,1). Next, we use the technique of random restrictions, used to prove AC^0 lower bounds, to prove a tight lower bound of Omega(1/epsilon^2) on computing a (1 +/- epsilon)-approximation to the sum of the nodes\u27 inputs. Our techniques are general, and apply to many types of radio channels studied in the literature
Erasure Correction for Noisy Radio Networks
The radio network model is a well-studied model of wireless, multi-hop networks. However, radio networks make the strong assumption that messages are delivered deterministically. The recently introduced noisy radio network model relaxes this assumption by dropping messages independently at random.
In this work we quantify the relative computational power of noisy radio networks and classic radio networks. In particular, given a non-adaptive protocol for a fixed radio network we show how to reliably simulate this protocol if noise is introduced with a multiplicative cost of poly(log Delta, log log n) rounds where n is the number nodes in the network and Delta is the max degree. Moreover, we demonstrate that, even if the simulated protocol is not non-adaptive, it can be simulated with a multiplicative O(Delta log ^2 Delta) cost in the number of rounds. Lastly, we argue that simulations with a multiplicative overhead of o(log Delta) are unlikely to exist by proving that an Omega(log Delta) multiplicative round overhead is necessary under certain natural assumptions
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
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
Broadcasting in Noisy Radio Networks
The widely-studied radio network model [Chlamtac and Kutten, 1985] is a
graph-based description that captures the inherent impact of collisions in
wireless communication. In this model, the strong assumption is made that node
receives a message from a neighbor if and only if exactly one of its
neighbors broadcasts.
We relax this assumption by introducing a new noisy radio network model in
which random faults occur at senders or receivers. Specifically, for a constant
noise parameter , either every sender has probability of
transmitting noise or every receiver of a single transmission in its
neighborhood has probability of receiving noise.
We first study single-message broadcast algorithms in noisy radio networks
and show that the Decay algorithm [Bar-Yehuda et al., 1992] remains robust in
the noisy model while the diameter-linear algorithm of Gasieniec et al., 2007
does not. We give a modified version of the algorithm of Gasieniec et al., 2007
that is robust to sender and receiver faults, and extend both this modified
algorithm and the Decay algorithm to robust multi-message broadcast algorithms.
We next investigate the extent to which (network) coding improves throughput
in noisy radio networks. We address the previously perplexing result of Alon et
al. 2014 that worst case coding throughput is no better than worst case routing
throughput up to constants: we show that the worst case throughput performance
of coding is, in fact, superior to that of routing -- by a
gap -- provided receiver faults are introduced. However, we show that any
coding or routing scheme for the noiseless setting can be transformed to be
robust to sender faults with only a constant throughput overhead. These
transformations imply that the results of Alon et al., 2014 carry over to noisy
radio networks with sender faults.Comment: Principles of Distributed Computing 201