Algorithms for Noisy Broadcast under Erasures

08/02/2018
by   Ofer Grossman, et al.
0

The noisy broadcast model was first studied in [Gallager, TranInf'88] where an n-character input is distributed among n processors, so that each processor receives one input bit. Computation proceeds in rounds, where in each round each processor broadcasts a single character, and each reception is corrupted independently at random with some probability p. [Gallager, TranInf'88] gave an algorithm for all processors to learn the input in O( n) rounds with high probability. Later, a matching lower bound of Ω( n) was given in [Goyal, Kindler, Saks; SICOMP'08]. We study a relaxed version of this model where each reception is erased and replaced with a `?' independently with probability p. In this relaxed model, we break past the lower bound of [Goyal, Kindler, Saks; SICOMP'08] and obtain an O(^* n)-round algorithm for all processors to learn the input with high probability. We also show an O(1)-round algorithm for the same problem when the alphabet size is Ω(poly(n)).

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/19/2019

Broadcast Congested Clique: Planted Cliques and Pseudorandom Generators

We develop techniques to prove lower bounds for the BCAST(log n) Broadca...
research
07/15/2018

Consensus Needs Broadcast in Noiseless Models but can be Exponentially Easier in the Presence of Noise

Consensus and Broadcast are two fundamental problems in distributed comp...
research
10/21/2019

A King in every two consecutive tournaments

We think of a tournament T=([n], E) as a communication network where in ...
research
02/26/2020

Quantum Distributed Complexity of Set Disjointness on a Line

Given x,y∈{0,1}^n, Set Disjointness consists in deciding whether x_i=y_i...
research
08/11/2022

Smoothed Analysis of Information Spreading in Dynamic Networks

The best known solutions for k-message broadcast in dynamic networks of ...
research
05/20/2022

(Poly)Logarithmic Time Construction of Round-optimal n-Block Broadcast Schedules for Broadcast and irregular Allgather in MPI

We give a fast(er), communication-free, parallel construction of optimal...
research
07/24/2020

Tight Distributed Sketching Lower Bound for Connectivity

In this paper, we study the distributed sketching complexity of connecti...

Please sign up or login with your details

Forgot password? Click here to reset