Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Alkema, Henk; de Berg, Mark https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-138081
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Rectilinear Steiner Trees in Narrow Strips

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Abstract

A rectilinear Steiner tree for a set P of points in ℝ² is a tree that connects the points in P using horizontal and vertical line segments. The goal of {Minimum Rectilinear Steiner Tree} is to find a rectilinear Steiner tree with minimal total length. We investigate how the complexity of {Minimum Rectilinear Steiner Tree} for point sets P inside the strip (-∞,+∞)× [0,δ] depends on the strip width δ. We obtain two main results.
- We present an algorithm with running time n^O(√δ) for sparse point sets, that is, point sets where each 1×δ rectangle inside the strip contains O(1) points.
- For random point sets, where the points are chosen randomly inside a rectangle of height δ and expected width n, we present an algorithm that is fixed-parameter tractable with respect to δ and linear in n. It has an expected running time of 2^{O(δ √{δ})} n.

BibTeX - Entry

@InProceedings{alkema_et_al:LIPIcs.SoCG.2021.9,
  author =	{Alkema, Henk and de Berg, Mark},
  title =	{{Rectilinear Steiner Trees in Narrow Strips}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13808},
  URN =		{urn:nbn:de:0030-drops-138081},
  doi =		{10.4230/LIPIcs.SoCG.2021.9},
  annote =	{Keywords: Computational geometry, fixed-parameter tractable algorithms}
}

Keywords: Computational geometry, fixed-parameter tractable algorithms
Seminar: 37th International Symposium on Computational Geometry (SoCG 2021)
Issue date: 2021
Date of publication: 02.06.2021


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