Shortest two disjoint paths in conservative graphs

Autor:	Schlotter, Ildikó
Rok vydání:	2023
Předmět:	Computer Science - Data Structures and Algorithms 05C85 (Primary) 68W05 05C38 (Secondary) G.2.2 F.2.2
Druh dokumentu:	Working Paper
Popis:	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 Seb\H{o} (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 $G$. Comment: A version of this paper has been accepted to the 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2307.12602 Zobrazit plný text záznamu View this record from Arxiv