A Refutation of Elmasry's $\tilde{O}(m \sqrt{n})$-Time Algorithm for Single-Source Shortest Paths
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916884937441280 |
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| author | Atalig, Sunny Chrobak, Marek |
| author_facet | Atalig, Sunny Chrobak, Marek |
| contents | In this note we examine the recent paper "Breaking the Bellman-Ford Shortest-Path Bound" by Amr Elmasry, where he presents an algorithm for the single-source shortest path problem and claims that its running time complexity is $\tilde{O}(m\sqrt{n})$, where $n$ is the number of vertices and $m$ is the number of edges. We show that his analysis is incorrect, by providing an example of a weighted graph on which the running time of his algorithm is $Ω(mn)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Refutation of Elmasry's $\tilde{O}(m \sqrt{n})$-Time Algorithm for Single-Source Shortest Paths Atalig, Sunny Chrobak, Marek Data Structures and Algorithms In this note we examine the recent paper "Breaking the Bellman-Ford Shortest-Path Bound" by Amr Elmasry, where he presents an algorithm for the single-source shortest path problem and claims that its running time complexity is $\tilde{O}(m\sqrt{n})$, where $n$ is the number of vertices and $m$ is the number of edges. We show that his analysis is incorrect, by providing an example of a weighted graph on which the running time of his algorithm is $Ω(mn)$. |
| title | A Refutation of Elmasry's $\tilde{O}(m \sqrt{n})$-Time Algorithm for Single-Source Shortest Paths |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2508.04872 |