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A Polynomial Time Algorithm for Steiner Tree When Terminals Avoid a Rooted K₄-Minor

Authors Carla Groenland , Jesper Nederlof , Tomohiro Koana

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  • Mathematics of computing → Graph algorithms
Keywords
  • Steiner tree
  • rooted minor

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Abstract

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(n⁴) 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.

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Carla Groenland, Jesper Nederlof, and Tomohiro Koana. A Polynomial Time Algorithm for Steiner Tree When Terminals Avoid a Rooted K₄-Minor. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.IPEC.2024.12

Author Details

Carla Groenland
  • Delft Institute of Applied Mathematics, The Netherlands
Jesper Nederlof
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Tomohiro Koana
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands

Funding

The work of both JN and TK has been supported by the project CRACKNP that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 853234).

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