Improved upper bounds on the reflexivity of point sets

Authors:
Eyal Ackerman;Oswin Aichholzer;Balázs Keszegh
Affiliations:
School of Computing Science, Simon Fraser University, Burnaby, BC, Canada;Institute for Software Technology, Graz University of Technology, Austria;Department of Mathematics and its Applications, Central European University, Budapest, Hungary
Venue:
Computational Geometry: Theory and Applications
Year:
2009

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Abstract

Given a set S of n points in the plane, the reflexivity of S, @r(S), is the minimum number of reflex vertices in a simple polygonalization of S. Arkin et al. [E.M. Arkin, S.P. Fekete, F. Hurtado, J.S.B. Mitchell, M. Noy, V. Sacristan, S. Sethia, On the reflexivity of point sets, in: B. Aronov, S. Basu, J. Pach M. Sharir (Eds.), Discrete and Computational Geometry: The Goodman-Pollack Festschrift, Springer, 2003, pp. 139-156] proved that @r(S)=