2026-08-10T17:31:11Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6047 2024-03-06T10:37:31Z ddc:004 open_access

A Plane 1.88-Spanner for Points in Convex Position Amani, Mahdi Biniaz, Ahmad Bose, Prosenjit De Carufel, Jean-Lou Maheshwari, Anil Smid, Michiel points in convex position plane spanner 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). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mahdi Amani and Ahmad Biniaz and Prosenjit Bose and Jean-Lou De Carufel and Anil Maheshwari and Michiel Smid 2016 Is Part Of LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SWAT.2016.25 urn:nbn:de:0030-drops-60474 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.25 eng https://creativecommons.org/licenses/by/3.0/legalcode