Breaking the Bellman-Ford Shortest-Path Bound
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929569421852672 |
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| author | Elmasry, Amr |
| author_facet | Elmasry, Amr |
| contents | In this paper we give a single-source shortest-path algorithm that breaks, after over 65 years, the $O(n \cdot m)$ bound for the running time of the Bellman-Ford-Moore algorithm, where $n$ is the number of vertices and $m$ is the number of arcs of the graph. Our algorithm converts the input graph to a graph with nonnegative weights by performing at most $\min(2 \cdot \sqrt{n},2 \cdot \sqrt{m/\log n})$ calls to a modified version of Dijkstra's algorithm, such that the shortest-path trees are the same for the new graph as those for the original. When Dijkstra's algorithm is implemented using Fibonacci heaps, the running time of our algorithm is therefore $O(\sqrt{n} \cdot m + n \cdot \sqrt{m \log n})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Breaking the Bellman-Ford Shortest-Path Bound Elmasry, Amr Data Structures and Algorithms In this paper we give a single-source shortest-path algorithm that breaks, after over 65 years, the $O(n \cdot m)$ bound for the running time of the Bellman-Ford-Moore algorithm, where $n$ is the number of vertices and $m$ is the number of arcs of the graph. Our algorithm converts the input graph to a graph with nonnegative weights by performing at most $\min(2 \cdot \sqrt{n},2 \cdot \sqrt{m/\log n})$ calls to a modified version of Dijkstra's algorithm, such that the shortest-path trees are the same for the new graph as those for the original. When Dijkstra's algorithm is implemented using Fibonacci heaps, the running time of our algorithm is therefore $O(\sqrt{n} \cdot m + n \cdot \sqrt{m \log n})$. |
| title | Breaking the Bellman-Ford Shortest-Path Bound |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2410.23383 |