License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2016.39
URN: urn:nbn:de:0030-drops-59310
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5931/
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Fomin, Fedor ; Kolay, Sudeshna ; Lokshtanov, Daniel ; Panolan, Fahad ; Saurabh, Saket

Subexponential Algorithms for Rectilinear Steiner Tree and Arborescence Problems

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Abstract

A rectilinear Steiner tree for a set T of points in the plane is a tree which connects T using horizontal and vertical lines. In the Rectilinear Steiner Tree problem, input is a set T of n points in the Euclidean plane (R^2) and the goal is to find an rectilinear Steiner tree for T of smallest possible total length. A rectilinear Steiner arborecence for a set T of points and root r in T is a rectilinear Steiner tree S for T such that the path in S from r to any point t in T is a shortest path. In the Rectilinear Steiner Arborescense problem the input is a set T of n points in R^2, and a root r in T, the task is to find an rectilinear Steiner arborescence for T, rooted at r of smallest possible total length. In this paper, we give the first subexponential time algorithms for both problems. Our algorithms are deterministic and run in 2^{O(sqrt{n}log n)} time.

BibTeX - Entry

@InProceedings{fomin_et_al:LIPIcs:2016:5931,
  author =	{Fedor Fomin and Sudeshna Kolay and Daniel Lokshtanov and Fahad Panolan and Saket Saurabh},
  title =	{{Subexponential Algorithms for Rectilinear Steiner Tree and Arborescence Problems}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{39:1--39:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{S{\'a}ndor Fekete and Anna Lubiw},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5931},
  URN =		{urn:nbn:de:0030-drops-59310},
  doi =		{10.4230/LIPIcs.SoCG.2016.39},
  annote =	{Keywords: Rectilinear graphs, Steiner arborescence, parameterized algorithms}
}

Keywords: Rectilinear graphs, Steiner arborescence, parameterized algorithms
Collection: 32nd International Symposium on Computational Geometry (SoCG 2016)
Issue Date: 2016
Date of publication: 10.06.2016

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