A Polynomial Time Algorithm for Steiner Tree when Terminals Avoid a $K_4$-Minor

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Groenland, Carla, Nederlof, Jesper, Koana, Tomohiro
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866912065087602688
author Groenland, Carla
Nederlof, Jesper
Koana, Tomohiro
author_facet Groenland, Carla
Nederlof, Jesper
Koana, Tomohiro
contents We study a special case of the Steiner Tree problem in which the input graph does not have a minor model of a complete graph on 4 vertices for which all branch sets contain a terminal. We show that this problem can be solved in $O(n^4)$ time, where $n$ denotes the number of vertices in the input graph. This generalizes a seminal paper by Erickson et al. [Math. Oper. Res., 1987] that solves Steiner tree on planar graphs with all terminals on one face in polynomial time.
format Preprint
id arxiv_https___arxiv_org_abs_2410_06793
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Polynomial Time Algorithm for Steiner Tree when Terminals Avoid a $K_4$-Minor
Groenland, Carla
Nederlof, Jesper
Koana, Tomohiro
Data Structures and Algorithms
We study a special case of the Steiner Tree problem in which the input graph does not have a minor model of a complete graph on 4 vertices for which all branch sets contain a terminal. We show that this problem can be solved in $O(n^4)$ time, where $n$ denotes the number of vertices in the input graph. This generalizes a seminal paper by Erickson et al. [Math. Oper. Res., 1987] that solves Steiner tree on planar graphs with all terminals on one face in polynomial time.
title A Polynomial Time Algorithm for Steiner Tree when Terminals Avoid a $K_4$-Minor
topic Data Structures and Algorithms
url https://arxiv.org/abs/2410.06793