Work

Shortest Two Disjoint Paths in Conservative Graphs

Year: 2026

Type: article

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 .

Source: Algorithmica

DOI: 10.1007/s00453-026-01375-7

Author: Ildikó Schlotter

Institutions: Eötvös Loránd University, Budapest University of Technology and Economics, ELTE Centre for Economic and Regional Studies

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Magyar Tudományos Akadémia, Eötvös Loránd Tudományegyetem