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  Linear-Time Triangulation of a Simple Polygon Made Easier Via Randomization

Amato, N. M., Goodrich, M. T., & Ramos, E. A. (2000). Linear-Time Triangulation of a Simple Polygon Made Easier Via Randomization. In Proceedings of the 16th Annual Symposium on Computational Geometry (SCG-00) (pp. 201-212). New York, USA: ACM Press.

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 Creators:
Amato, Nancy M., Author
Goodrich, Michael T., Author
Ramos, Edgar A.1, Author           
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: We describe a randomized algorithm for computing the trapezoidal decomposition of a simple polygon. Its expected running time is linear in the size of the polygon. By a well-known and simple linear time reduction, this implies a linear time algorithm for triangulating a simple polygon. Our algorithm is considerably simpler than Chazelle's (1991) celebrated optimal deterministic algorithm and, hence, positively answers his question of whether a simpler randomized algorithm for the problem exists. The new algorithm can be viewed as a combination of Chazelle's algorithm and of non-optimal randomized algorithms due to Clarkson {\it et al.} (1991) and to Seidel (1991), with the essential innovation that sampling is performed on subchains of the initial polygonal chain, rather than on its edges. It is also essential, as in Chazelle's algorithm, to include a bottom-up preprocessing phase previous to the top-down construction phase.

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Language(s): eng - English
 Dates: 2010-03-022000
 Publication Status: Issued
 Pages: -
 Publishing info: New York, USA : ACM Press
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 518132
URI: http://www.mpi-sb.mpg.de/~ramos
Other: Local-ID: C1256428004B93B8-087911021E0767A8C12569FC005796C3-Ramos2000a
 Degree: -

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Title: Untitled Event
Place of Event: Clear Water Bay, Kowloon, Hong Kong
Start-/End Date: 2000-06-12 - 2000-06-14

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Title: Proceedings of the 16th Annual Symposium on Computational Geometry (SCG-00)
Source Genre: Proceedings
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Publ. Info: New York, USA : ACM Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 201 - 212 Identifier: -