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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Keywords Plane spanner, Points in convex position
Persistent URL dx.doi.org/10.4230/LIPIcs.SWAT.2016.25
Conference 15th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2016
Amani, M. (Mahdi), Biniaz, A. (Ahmad), Bose, P, De Carufel, J.-L. (Jean-Lou), Maheshwari, A, & Smid, M. (2016). A plane 1.88-spanner for points in convex position. In Leibniz International Proceedings in Informatics, LIPIcs (pp. 25.1–25.14). doi:10.4230/LIPIcs.SWAT.2016.25