Byzantine Fireflies

This paper addresses the problem of synchronous beeping, as addressed by swarms of fireflies. We present Byzantine-resilient algorithms ensuring that the correct processes eventually beep synchronously despite a subset of nodes beeping asynchronously. We assume that n > 2f (n is the number of processes and f is the number of Byzantine processes) and that the initial state of the processes can be arbitrary (self-stabilization). We distinguish the cases where the beeping period is known, unknown or approximately known. We also consider the situation where the processes can produce light continuously. © Springer-Verlag Berlin Heidelberg 2015

Byzantine Fireflies

This paper addresses the problem of synchronous beeping, as addressed by swarms of fireflies. We present Byzantine-resilient algorithms ensuring that the correct processes eventually beep synchronously despite a subset of nodes beeping asynchronously. We assume that $n > 2f$ ($n$ is the number of processes and $f$ is the number of Byzantine processes) and that the initial state of the processes can be arbitrary (self-stabilization). We distinguish the cases where the beeping period is known, unknown or approximately known. We also consider the situation where the processes can produce light continuously

Beeping a Deterministic Time-Optimal Leader Election

The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. In this model, we solve the leader election problem with an asymptotically optimal round complexity of O(D + log n), for a network of unknown size n and unknown diameter D (but with unique identifiers). Contrary to the best previously known algorithms in the same setting, the proposed one is deterministic. The techniques we introduce give a new insight as to how local constraints on the exchangeable messages can result in efficient algorithms, when dealing with the beeping model. Using this deterministic leader election algorithm, we obtain a randomized leader election algorithm for anonymous networks with an asymptotically optimal round complexity of O(D + log n) w.h.p. In previous works this complexity was obtained in expectation only. Moreover, using deterministic leader election, we obtain efficient algorithms for symmetry-breaking and communication procedures: O(log n) time MIS and 5-coloring for tree networks (which is time-optimal), as well as k-source multi-broadcast for general graphs in O(min(k,log n) * D + k log{(n M)/k}) rounds (for messages in {1,..., M}). This latter result improves on previous solutions when the number of sources k is sublogarithmic (k = o(log n))

Noisy Beeping Networks

We introduce noisy beeping networks, where nodes have limited communication capabilities, namely, they can only emit energy or sense the channel for energy. Furthermore, imperfections may cause devices to malfunction with some fixed probability when sensing the channel, which amounts to deducing a noisy received transmission. Such noisy networks have implications for ultra-lightweight sensor networks and biological systems. We show how to compute tasks in a noise-resilient manner over noisy beeping networks of arbitrary structure. In particular, we transform any algorithm that assumes a noiseless beeping network (of size $n$) into a noise-resilient version while incurring a multiplicative overhead of only $O(\log n)$ in its round complexity, with high probability. We show that our coding is optimal for some tasks, such as node-coloring of a clique. We further show how to simulate a large family of algorithms designed for distributed networks in the CONGEST($B$) model over a noisy beeping network. The simulation succeeds with high probability and incurs an asymptotic multiplicative overhead of $O(B\cdot \Delta \cdot \min(n,\Delta^2))$ in the round complexity, where $\Delta$ is the maximal degree of the network. The overhead is tight for certain graphs, e.g., a clique. Further, this simulation implies a constant overhead coding for constant-degree networks