2026-08-10T22:48:42Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24946 2026-02-09T08:02:26Z ddc:004 open_access

Structural Parameters for Steiner Orientation Hanaka, Tesshu Lampis, Michael Melissinos, Nikolaos Nemery, Edouard Ono, Hirotaka Vasilakis, Manolis ETH Steiner Orientation Treewidth 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). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tesshu Hanaka and Michael Lampis and Nikolaos Melissinos and Edouard Nemery and Hirotaka Ono and Manolis Vasilakis 2025 Is Part Of LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2025.38 urn:nbn:de:0030-drops-249461 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.38 eng https://creativecommons.org/licenses/by/4.0/legalcode