Structural Parameters for Steiner Orientation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10512012" target="_blank" >RIV/00216208:11320/25:10512012 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.ISAAC.2025.38" target="_blank" >https://doi.org/10.4230/LIPIcs.ISAAC.2025.38</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2025.38" target="_blank" >10.4230/LIPIcs.ISAAC.2025.38</a>

Result language

angličtina

Original language name

Structural Parameters for Steiner Orientation

Original language description

We consider the Steiner Orientation problem, where we are given as input a mixed graph G = (V,E,A) and a set of k demand pairs (s_i,t_i), i ∈ [k]. The goal is to orient the undirected edges of G in a way that the resulting directed graph has a directed path from s_i to t_i for all i ∈ [k]. We adopt the point of view of structural parameterized complexity and investigate the complexity of Steiner Orientation for standard measures, such as treewidth. Our results indicate that Steiner Orientation is a surprisingly hard problem from this point of view. In particular, our main contributions are the following:1) We show that Steiner Orientation is NP-complete on instances where the underlying graph has feedback vertex number 2, treewidth 2, pathwidth 3, and vertex integrity 6.2) We present an XP algorithm parameterized by vertex cover number vc of complexity n^O(vc²). Furthermore, we show that this running time is essentially optimal by proving that a running time of n^o(vc²) would refute the ETH.3) We consider parameterizations by the number of undirected or directed edges (|E| or |A|) and we observe that the trivial 2^|E| n^O(1)-time algorithm for the former parameter is optimal under the SETH. Complementing this, we show that the problem admits a 2^O(|A|) n^O(1)-time algorithm.In addition to the above, we consider the complexity of Steiner Orientation parameterized by tw+k (FPT), distance to clique (FPT), and vc+k (FPT with a polynomial kernel).

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GA25-17221S" target="_blank" >GA25-17221S: New Models of Trust and Voting Robustness in Large Multiagent Systems</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-408-6

ISSN

1868-8969

e-ISSN

1868-8969

Number of pages

14

Pages from-to

—

Publisher name

Schloss Dagstuhl, Leibniz-Zentrum für Informatik

Place of publication

Wadern

Event location

ISAAC 2025

Event date

Dec 7, 2025

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

—