Copyright © 2003 Published by Elsevier B.V.
Notes
The cost of cutting out convex n-gons
Received 29 April 2002;
Revised 2 January 2003;
accepted 24 September 2003.
Available online 19 December 2003.
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Abstract
Given a convex n-gon P drawn on a piece of paper Q of unit diameter we prove that it can be cut with a total cost of O(log n). This bound is shown to be asymptotically tight: a regular n-gon (whose circumscribed circle has radius, say, 1/3) drawn on a square piece of paper of unit diameter requires a cut cost of Ω(log n).
Author Keywords: Combinatorial geometry; Complexity of cutting; Convex polygons







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