NDLI: Polygons Needing Many Flipturns

Content Provider	Springer Nature Link
Author	Biedl, Therese
Copyright Year	2005
Abstract	A flipturn on a polygon consists of reversing the order of edges inside a pocket of the polygon, without changing lengths or slopes. Any polygon with n edges must be convexified after at most (n − 1)! flipturns. A recent paper showed that in fact it will be convex after at most n(n−3)/2 flipturns.We give here lower bounds.We construct a polygon such that if pockets are chosen in a bad way, at least (n − 2)2/4 flipturns are needed to convexify the polygon. In another construction, (n −1)2/8 flipturns are needed, regardless of the order in which pockets are chosen. All our bounds are adaptive to a pre-specified number of distinct slopes of the edges.
Starting Page	131
Ending Page	141
Page Count	11
File Format	PDF
ISSN	01795376
Journal	Discrete & Computational Geometry
Volume Number	35
Issue Number	1
e-ISSN	14320444
Language	English
Publisher	Springer-Verlag
Publisher Date	2005-09-19
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computational Mathematics and Numerical Analysis Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science Computational Theory and Mathematics Geometry and Topology

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Polygons Needing Many Flipturns