Reducing Shortcut and Hopset Constructions to Shallow Graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912557595361280 |
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| author | Haeupler, Bernhard Jiang, Yonggang Saranurak, Thatchaphol |
| author_facet | Haeupler, Bernhard Jiang, Yonggang Saranurak, Thatchaphol |
| contents | 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 $h$ to assume the input graph $G$ is ``shallow'', meaning if vertex $s$ can reach vertex $t$, it can do so in approximately $h$ 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 ]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reducing Shortcut and Hopset Constructions to Shallow Graphs Haeupler, Bernhard Jiang, Yonggang Saranurak, Thatchaphol Data Structures and Algorithms 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 $h$ to assume the input graph $G$ is ``shallow'', meaning if vertex $s$ can reach vertex $t$, it can do so in approximately $h$ 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 ]. |
| title | Reducing Shortcut and Hopset Constructions to Shallow Graphs |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2508.20302 |