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Algorithms for Noisy Broadcast with Erasures

Authors Ofer Grossman, Bernhard Haeupler, Sidhanth Mohanty

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ACM Subject Classification
  • Theory of computation → Distributed computing models
Keywords
  • noisy broadcast
  • error correction
  • erasures
  • distributed computing with noise

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Abstract

The noisy broadcast model was first studied by [Gallager, 1988] 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, 1988] gave an algorithm for all processors to learn the input in O(log log n) rounds with high probability. Later, a matching lower bound of Omega(log log n) was given by [Goyal et al., 2008].
We study a relaxed version of this model where each reception is erased and replaced with a `?' independently with probability p, so the processors have knowledge of whether a bit has been corrupted. In this relaxed model, we break past the lower bound of [Goyal et al., 2008] and obtain an O(log^* 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 Omega(poly(n)).

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Ofer Grossman, Bernhard Haeupler, and Sidhanth Mohanty. Algorithms for Noisy Broadcast with Erasures. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 153:1-153:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ICALP.2018.153

Author Details

Ofer Grossman
  • EECS Departent, MIT, Cambridge, MA, USA
Bernhard Haeupler
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA
Sidhanth Mohanty
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA

References

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