Loading…

Adaptive Massively Parallel Connectivity in Optimal Space

We study the problem of finding connected components in the Adaptive Massively Parallel Computation (AMPC) model. We show that when we require the total space to be linear in the size of the input graph the problem can be solved in \(O(\log^* n)\) rounds in forests (with high probability) and \(2^{O...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-04
Main Authors: Latypov, Rustam, Łącki, Jakub, Maus, Yannic, Uitto, Jara
Format: Article
Language:English
Subjects:
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the problem of finding connected components in the Adaptive Massively Parallel Computation (AMPC) model. We show that when we require the total space to be linear in the size of the input graph the problem can be solved in \(O(\log^* n)\) rounds in forests (with high probability) and \(2^{O(\log^* n)}\) expected rounds in general graphs. This improves upon an existing \(O(\log \log_{m/n} n)\) round algorithm. For the case when the desired number of rounds is constant we show that both problems can be solved using \(\Theta(m + n \log^{(k)} n)\) total space in expectation (in each round), where \(k\) is an arbitrarily large constant and \(\log^{(k)}\) is the \(k\)-th iterate of the \(\log_2\) function. This improves upon existing algorithms requiring \(\Omega(m + n \log n)\) total space.
ISSN:2331-8422
DOI:10.48550/arxiv.2302.04033