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arXiv · 2605.03892

Parallel Reachability and Shortest Paths on Non-sparse Digraphs: Near-linear Work and Sub-square-root Depth

Vikrant Ashvinkumar·Aaron Bernstein·Maximilian Probst Gutenberg·Thatchaphol Saranurak
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Abstract

We present parallel algorithms for computing single-source reachability and shortest paths on directed $n$-vertex $m$-edge graphs using near-linear $\tilde{O}(m)$ work and $o(\sqrt{n})$ depth whenever $m\ge n^{1+o(1)}$. At the extreme of $m=\Omega(n^{2})$, our reachability and shortest path algorithms have depth only $n^{0.136}$ and $n^{0.25+o(1)}$, respectively. The state-of-the-art parallel algorithms with near-linear work for both problems require $\Omega(\sqrt{n})$ depth in all density regimes.

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Vikrant Ashvinkumar, Aaron Bernstein, Maximilian Probst Gutenberg, Thatchaphol Saranurak. 2026-05-05. Parallel Reachability and Shortest Paths on Non-sparse Digraphs: Near-linear Work and Sub-square-root Depth. https://arxiv.org/abs/2605.03892

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