On the Complexity of Finding Internally Vertex-Disjoint Long Directed Paths - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles Algorithmica Year : 2020

On the Complexity of Finding Internally Vertex-Disjoint Long Directed Paths

Abstract

For two positive integers k and , a (k ×)-spindle is the union of k pairwise internally vertex-disjoint directed paths with arcs each between two vertices u and v. We are interested in the (parameterized) complexity of several problems consisting in deciding whether a given digraph contains a subdivision of a spindle, which generalize both the Maximum Flow and Longest Path problems. We obtain the following complexity dichotomy: for a fixed ≥ 1, finding the largest k such that an input digraph G contains a subdivision of a (k ×)-spindle is polynomial-time solvable if ≤ 3, and NP-hard otherwise. We place special emphasis on finding spindles with exactly two paths and present FPT algorithms that are asymptotically optimal under the ETH. These algorithms are based on the technique of representative families in matroids, and use also color-coding as a subroutine. Finally, we study the case where the input graph is acyclic, and present several algorithmic and hardness results.
Fichier principal
Vignette du fichier
ALGO-D-19-00018-R1.pdf (816.66 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

lirmm-02989813 , version 1 (05-11-2020)

Licence

Attribution

Identifiers

Cite

Júlio Araújo, Victor A Campos, Ana Karolinna Maia de Oliveira, Ignasi Sau, Ana Silva. On the Complexity of Finding Internally Vertex-Disjoint Long Directed Paths. Algorithmica, 2020, 82 (6), pp.1616-1639. ⟨10.1007/s00453-019-00659-5⟩. ⟨lirmm-02989813⟩
24 View
63 Download

Altmetric

Share

Gmail Facebook X LinkedIn More