We show an improved parallel algorithm for decomposing an undirected unweighted graph into small diameter pieces with a small fraction of the edges in between. These decompositions form critical subroutines in a number of graph algorithms. Our algorithm builds upon the shifted shortest path approach introduced in [Blelloch, Gupta, Koutis, Miller, Peng, Tangwongsan, SPAA 2011]. By combining various stages of the previous algorithm, we obtain a significantly simpler algorithm with the same asymptotic guarantees as the best sequential algorithm.
@article{arxiv.1307.3692,
title = {Parallel Graph Decompositions Using Random Shifts},
author = {Gary L. Miller and Richard Peng and Shen Chen Xu},
journal= {arXiv preprint arXiv:1307.3692},
year = {2013}
}