Shortest two disjoint paths in conservative graphs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913189249155072 |
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| author | Schlotter, Ildikó |
| author_facet | Schlotter, Ildikó |
| contents | We consider the following problem that we call the Shortest Two Disjoint Paths problem: given an undirected graph $G=(V,E)$ with edge weights $w:E \rightarrow \mathbb{R}$, two terminals $s$ and $t$ in $G$, find two internally vertex-disjoint paths between $s$ and $t$ with minimum total weight. As shown recently by Schlotter and Sebő (2022), this problem becomes NP-hard if edges can have negative weights, even if the weight function is conservative, there are no cycles in $G$ with negative total weight. We propose a polynomial-time algorithm that solves the Shortest Two Disjoint Paths problem for conservative weights in the case when the negative-weight edges form a constant number of trees in $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12602 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shortest two disjoint paths in conservative graphs Schlotter, Ildikó Data Structures and Algorithms 05C85 (Primary) 68W05, 05C38 (Secondary) G.2.2; F.2.2 We consider the following problem that we call the Shortest Two Disjoint Paths problem: given an undirected graph $G=(V,E)$ with edge weights $w:E \rightarrow \mathbb{R}$, two terminals $s$ and $t$ in $G$, find two internally vertex-disjoint paths between $s$ and $t$ with minimum total weight. As shown recently by Schlotter and Sebő (2022), this problem becomes NP-hard if edges can have negative weights, even if the weight function is conservative, there are no cycles in $G$ with negative total weight. We propose a polynomial-time algorithm that solves the Shortest Two Disjoint Paths problem for conservative weights in the case when the negative-weight edges form a constant number of trees in $G$. |
| title | Shortest two disjoint paths in conservative graphs |
| topic | Data Structures and Algorithms 05C85 (Primary) 68W05, 05C38 (Secondary) G.2.2; F.2.2 |
| url | https://arxiv.org/abs/2307.12602 |