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Discrete Applied Mathematics
Volume 143, Issues 1-3, 30 September 2004, Pages 353-358
 
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doi:10.1016/j.dam.2003.09.001    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2003 Published by Elsevier B.V.

Notes

The cost of cutting out convex n-gons

Adrian DumitrescuE-mail The Corresponding Author

Computer Science, University of Wisconsin–Milwaukee, Milwaukee, WI 53201-0784, USA

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

Article Outline

1. Introduction
2. Proof of Theorem 1
3. Conclusion
References







Discrete Applied Mathematics
Volume 143, Issues 1-3, 30 September 2004, Pages 353-358
 
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