LOWER BOUND FOR CONVEX HULL AREA AND UNIVERSAL COVER PROBLEMS-Reference-Cited by-同舟云学术

LOWER BOUND FOR CONVEX HULL AREA AND UNIVERSAL COVER PROBLEMS

Published:2013-06 Issue:03 Volume:23 Page:197-212
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

KHANDHAWIT TIRASAN¹,PAGONAKIS DIMITRIOS²,SRISWASDI SIRA³

Affiliation:

1. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

2. Massachusetts Institute of Technology, 428 Memorial Drive, Cambridge, MA 02139, USA

3. Graduate Group in Genomics and Computational Biology, University of Pennsylvania, Philadelphia, PA 19104, USA

Abstract

We provide a technique to obtain a lower bound for the area of the convex hull of a set of points and a rectangle in the plane, and then apply the resulting estimates to improve the lower bound for the convex case of Moser's Worm problem. Specifically, we show that any convex universal cover for unit arcs has an area of at least 0.232239. We also apply our approach to the universal cover problem for closed unit curves.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195913500076

Reference14 articles.

1. A LOWER BOUND FOR LEBESGUE'S UNIVERSAL COVER PROBLEM

2. Der zentralsymmetrische Kern und die zentralsymmetrische H�lle von konvexen K�rpern

3. Lost in a Forest

4. Covers for closed curves of length two

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