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Polygon triangulation in O (n log log n) time with simple data structures

Author: D G Kirkpatrick; Maria Klawe; Robert E Tarjan
Publisher: Vancouver, B.C., Canada : University of British Columbia, Dept. of Computer Science, [1990]
Series: University of British Columbia.; Department of Computer Science.; Technical report
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
Abstract: "We give a new O (n log log n)-time deterministic algorithm for triangulating simple n-vertex polygons, which avoids the use of complicated data structures. In addition, for polygons whose vertices have integer coordinates of polynomially bounded size, the algorithm can be modified to run in O (n log[superscript *] n) time. The major new techniques employed are the efficient location of horizontal
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Document Type: Book
All Authors / Contributors: D G Kirkpatrick; Maria Klawe; Robert E Tarjan
OCLC Number: 24301368
Notes: "June, 1990."
Description: 16 pages : illustrations ; 28 cm.
Series Title: University of British Columbia.; Department of Computer Science.; Technical report
Responsibility: by David G. Kirkpatrick, Maria M. Klawe, and Robert E. Tarjan.

Abstract:

Abstract: "We give a new O (n log log n)-time deterministic algorithm for triangulating simple n-vertex polygons, which avoids the use of complicated data structures. In addition, for polygons whose vertices have integer coordinates of polynomially bounded size, the algorithm can be modified to run in O (n log[superscript *] n) time. The major new techniques employed are the efficient location of horizontal visibility edges that partition the interior of the polygon into regions of approximately equal size, and a linear-time algorithm for obtaining the horizontal visibility partition of a subchain of a polygonal chain, from the horizontal visibilty partition of the entire chain.

The latter technique has other interesting applications, including a linear-time algorithm to convert a Steiner triangulation of a polygon into a true triangulation."

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