Binary weights spanning trees and the $k$-red spanning tree problem in linear time
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911758280556544 |
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| author | Hochbaum, Dorit S. |
| author_facet | Hochbaum, Dorit S. |
| contents | We address here spanning tree problems on a graph with binary edge weights. For a general weighted graph the minimum spanning tree is solved in super-linear running time, even when the edges of the graph are pre-sorted. A related problem, of finding a spanning tree with a pre-specified sum of weights, is NP-hard. In contrast, for a graph with binary weights associated with the edges, it is shown that the minimum spanning tree and finding a spanning tree with a given total sum, are solvable in linear time with simple algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Binary weights spanning trees and the $k$-red spanning tree problem in linear time Hochbaum, Dorit S. Data Structures and Algorithms We address here spanning tree problems on a graph with binary edge weights. For a general weighted graph the minimum spanning tree is solved in super-linear running time, even when the edges of the graph are pre-sorted. A related problem, of finding a spanning tree with a pre-specified sum of weights, is NP-hard. In contrast, for a graph with binary weights associated with the edges, it is shown that the minimum spanning tree and finding a spanning tree with a given total sum, are solvable in linear time with simple algorithms. |
| title | Binary weights spanning trees and the $k$-red spanning tree problem in linear time |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2401.07341 |