Strongly Polynomial Parallel Work-Depth Tradeoffs for Directed SSSP
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909864148598784 |
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| author | Karczmarz, Adam Nadara, Wojciech Sokołowski, Marek |
| author_facet | Karczmarz, Adam Nadara, Wojciech Sokołowski, Marek |
| contents | In this paper, we show new strongly polynomial work-depth tradeoffs for computing single-source shortest paths (SSSP) in non-negatively weighted directed graphs in parallel. Most importantly, we prove that directed SSSP can be solved within $\tilde{O}(m+n^{2-ε})$ work and $\tilde{O}(n^{1-ε})$ depth for some positive $ε>0$. In particular, for dense graphs with non-negative real weights, we provide the first nearly work-efficient strongly polynomial algorithm with sublinear depth.
Our result immediately yields improved strongly polynomial parallel algorithms for min-cost flow and the assignment problem. It also leads to the first non-trivial strongly polynomial dynamic algorithm for minimum mean cycle. Moreover, we develop efficient parallel algorithms in the Word RAM model for several variants of SSSP in graphs with exponentially large edge weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19780 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strongly Polynomial Parallel Work-Depth Tradeoffs for Directed SSSP Karczmarz, Adam Nadara, Wojciech Sokołowski, Marek Data Structures and Algorithms In this paper, we show new strongly polynomial work-depth tradeoffs for computing single-source shortest paths (SSSP) in non-negatively weighted directed graphs in parallel. Most importantly, we prove that directed SSSP can be solved within $\tilde{O}(m+n^{2-ε})$ work and $\tilde{O}(n^{1-ε})$ depth for some positive $ε>0$. In particular, for dense graphs with non-negative real weights, we provide the first nearly work-efficient strongly polynomial algorithm with sublinear depth. Our result immediately yields improved strongly polynomial parallel algorithms for min-cost flow and the assignment problem. It also leads to the first non-trivial strongly polynomial dynamic algorithm for minimum mean cycle. Moreover, we develop efficient parallel algorithms in the Word RAM model for several variants of SSSP in graphs with exponentially large edge weights. |
| title | Strongly Polynomial Parallel Work-Depth Tradeoffs for Directed SSSP |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2510.19780 |