Dartmouth logo Dartmouth College Computer Science
Technical Report series
CS home
TR home
TR search TR listserv
By author: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
By number: 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, 1997, 1996, 1995, 1994, 1993, 1992, 1991, 1990, 1989, 1988, 1987, 1986

Fast Greedy Triangulation Algorithms
Matthew T. Dickerson, Robert L. Scot Drysdale, Scott A. McElfresh, Emo Welzl
Dartmouth PCS-TR94-215

Abstract: The greedy triangulation of a set $S$ of $n$ points in the plane is the triangulation obtained by starting with the empty set and at each step adding the shortest compatible edge between two of the points, where a compatible edge is defined to be an edge that crosses none of the previously added edges. In this paper we present a simple, practical algorithm that computes the greedy triangulation in expected time $O(n \log n)$ and space $O(n)$ for points uniformly distributed over any convex shape. A variant of this algorithm should be fast for some other distributions. As part of this algorithm we give an edge compatiblity test that requires $O(n)$ time for both tests and updates to the underlying data structure. We also prove properties about the expected lengths of edges in greedy and Delaunay triangulations of uniformly distributed points.

PS.Z compressed postscript .ps.Z (104KB) , PDF PDF (280KB) (derived from the ps.Z)

Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]

Or copy and paste:
   Matthew T. Dickerson, Robert L. Scot Drysdale, Scott A. McElfresh, and Emo Welzl, "Fast Greedy Triangulation Algorithms." Dartmouth Computer Science Technical Report PCS-TR94-215, 1994.

Notify me about new tech reports.

Search the technical reports.

To receive paper copy of a report, by mail, send your address and the TR number to reports AT cs.dartmouth.edu

Copyright notice: The documents contained in this server are included by the contributing authors as a means to ensure timely dissemination of scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.

Technical reports collection maintained by David Kotz.