Adaptive Massively Parallel Connectivity in Optimal Space
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 February 2023
 DOI:
 10.48550/arXiv.2302.04033
 arXiv:
 arXiv:2302.04033
 Bibcode:
 2023arXiv230204033L
 Keywords:

 Computer Science  Distributed;
 Parallel;
 and Cluster Computing;
 Computer Science  Data Structures and Algorithms
 EPrint:
 ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) 2023