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DOI: 10.4230/LIPIcs.SWAT.2016.25

A Plane 1.88-Spanner for Points in Convex Position

Authors: Mahdi Amani, Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, Anil Maheshwari, and Michiel Smid

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

Abstract

Let S be a set of n points in the plane that is in convex position. For a real number t>1, we say that a point p in S is t-good if for every point q of S, the shortest-path distance between p and q along the boundary of the convex hull of S is at most t times the Euclidean distance between p and q. We prove that any point that is part of (an approximation to) the diameter of S is 1.88-good. Using this, we show how to compute a plane 1.88-spanner of S in O(n) time, assuming that the points of S are given in sorted order along their convex hull. Previously, the best known stretch factor for plane spanners was 1.998 (which, in fact, holds for any point set, i.e., even if it is not in convex position).

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Mahdi Amani, Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, Anil Maheshwari, and Michiel Smid. A Plane 1.88-Spanner for Points in Convex Position. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{amani_et_al:LIPIcs.SWAT.2016.25,
  author =	{Amani, Mahdi and Biniaz, Ahmad and Bose, Prosenjit and De Carufel, Jean-Lou and Maheshwari, Anil and Smid, Michiel},
  title =	{{A Plane 1.88-Spanner for Points in Convex Position}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.25},
  URN =		{urn:nbn:de:0030-drops-60474},
  doi =		{10.4230/LIPIcs.SWAT.2016.25},
  annote =	{Keywords: points in convex position, plane spanner}
}

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A Plane 1.88-Spanner for Points in Convex Position

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