Algorithms for Noisy Broadcast with Erasures

Ofer Grossman, Bernhard Haeupler, Sidhanth Mohanty, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
The noisy broadcast model was first studied by [10] 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. [10] 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 Ω(log log n) was
more » ... en by [11]. 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 [11] 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 Ω(poly(n)).
doi:10.4230/lipics.icalp.2018.153 dblp:conf/icalp/GrossmanHM18 fatcat:r5v3mywrofa6nf7zq5gz5rgeui