Shortest Two Disjoint Paths in Conservative Graphs
Abstract
Abstract We consider the following problem that we call the Shortest Two Disjoint Paths problem: given an undirected graph $$G=(V,E)$$ G = ( V , E ) with edge weight function $${w:E\rightarrow \mathbb {R}}$$ w : E → 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 $$\textsf{NP}$$ NP -hard if edges can have negative weights, even if the weight function is conservative, i.e., 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 .
Fields of Study & Subjects
Advanced Graph Theory Research
Complexity and Algorithms in Graphs
Limits and Structures in Graph Theory
Publication details
- Journal / source
- Algorithmica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 88
- Issue
- 2
- Publication date
- 21 March 2026
- Language
- EN