Given an undirected graph G of n weighted edges, stored one edge per processor in a square mesh of n processors, we show how to determine the connected components and a minimal spanning forest in Θ(n) time. More generally, we show how to solve these problems in Θ(n1/d) time when the mesh is a d-dimensional cube, where the implied constants depend upon d.
@article{arxiv.1502.01435,
title = {Optimal component labeling algorithms for mesh-connected computers and VLSI},
author = {Quentin F. Stout},
journal= {arXiv preprint arXiv:1502.01435},
year = {2015}
}