Showing papers by "Yehuda Afek published in 2018"

The Power of Multimedia: Combining Point-to-Point and Multiaccess Networks

Abstract: This paper introduces a new network model called a multimedia network. It combines the point-to-point message passing network and the multiaccess channel. To benefit from the combination, the designed algorithms consist of two stages: a local stage which utilizes the parallelism of the point-to-point network and a global stage which utilizes the broadcast capability of the multiaccess channel. To balance the complexities of the two stages a components each of radius O( 4 artition of the network into O(A) connected n) is required. We present efftcient deterministic and randomized partitioning algorithms that run in O(& log* n) time. The deterministic algorithm sends O(m + n log

A Wealth of Sub-Consensus Deterministic Objects.

Abstract: The consensus hierarchy classifies shared an object according to its consensus number, which is the maximum number of processes that can solve consensus wait-free using the object. The question of whether this hierarchy is precise enough to fully characterize the synchronization power of deterministic shared objects was open until 2016, when Afek et al. showed that there is an infinite hierarchy of deterministic objects, each weaker than the next, which is strictly between i and i + 1-processors consensus, for i ≥ 2. For i = 1, the question whether there exist a deterministic object whose power is strictly between read-write and 2-processors consensus, remained open. We resolve the question positively by exhibiting an infinite hierarchy of simple deterministic objects which are equivalent to set-consensus tasks, and thus are stronger than read-write registers, but they cannot implement consensus for two processes. Still our paper leaves a gap with open questions. 2012 ACM Subject Classification Theory of computation → Distributed computing models

Selecting a Leader in a Network of Finite State Machines.

Abstract: This paper studies a variant of the leader election problem under the stone age model (Emek and Wattenhofer, PODC 2013) that considers a network of n randomized finite automata with very weak communication capabilities (a multi-frequency asynchronous generalization of the beeping model's communication scheme). Since solving the classic leader election problem is impossible even in more powerful models, we consider a relaxed variant, referred to as k-leader selection, in which a leader should be selected out of at most k initial candidates. Our main contribution is an algorithm that solves k-leader selection for bounded k in the aforementioned stone age model. On (general topology) graphs of diameter D, this algorithm runs in O~(D) time and succeeds with high probability. The assumption that k is bounded turns out to be unavoidable: we prove that if k = omega (1), then no algorithm in this model can solve k-leader selection with a (positive) constant probability.

The Synergy of Finite State Machines

Abstract: What can be computed by a network of n randomized finite state machines communicating under the stone age model (Emek & Wattenhofer, PODC 2013)? The inherent linear upper bound on the total space of the network implies that its global computational power is not larger than that of a randomized linear space Turing machine, but is this tight? We answer this question affirmatively for bounded degree networks by introducing a stone age algorithm (operating under the most restrictive form of the model) that given a designated I/O node, constructs a tour in the network that enables the simulation of the Turing machine's tape. To construct the tour with high probability, we first show how to 2-hop color the network concurrently with building a spanning tree.

Selecting a Leader in a Network of Finite State Machines

Abstract: This paper studies a variant of the \emph{leader election} problem under the \emph{stone age} model (Emek and Wattenhofer, PODC 2013) that considers a network of $n$ randomized finite automata with very weak communication capabilities (a multi-frequency asynchronous generalization of the \emph{beeping} model's communication scheme). Since solving the classic leader election problem is impossible even in more powerful models, we consider a relaxed variant, referred to as \emph{$k$-leader selection}, in which a leader should be selected out of at most $k$ initial candidates. Our main contribution is an algorithm that solves $k$-leader selection for bounded $k$ in the aforementioned stone age model. On (general topology) graphs of diameter $D$, this algorithm runs in $\tilde{O}(D)$ time and succeeds with high probability. The assumption that $k$ is bounded turns out to be unavoidable: we prove that if $k = \omega (1)$, then no algorithm in this model can solve $k$-leader selection with a (positive) constant probability.