Reducing Shortcut and Hopset Constructions to Shallow Graphs
Abstract
We introduce a blackbox framework that simplifies all known parallel algorithms with near-linear work for single-source reachability and shortest paths in directed graphs. Specifically, existing reachability algorithms rely on constructing shortcuts; our blackbox allows these algorithms that construct shortcuts with hopbound to assume the input graph is ``shallow'', meaning if vertex can reach vertex , it can do so in approximately hops. This assumption significantly simplifies shortcut construction [Fin18, JLS19], resulting in simpler parallel reachability algorithms. Furthermore, our blackbox extends naturally to simplify parallel algorithms for constructing hopsets and, consequently, for computing shortest paths [CFR20 , CF23 , RHM+23 ].
Cite
@article{arxiv.2508.20302,
title = {Reducing Shortcut and Hopset Constructions to Shallow Graphs},
author = {Bernhard Haeupler and Yonggang Jiang and Thatchaphol Saranurak},
journal= {arXiv preprint arXiv:2508.20302},
year = {2025}
}