Discrete & Computational Geometry

, Volume 18, Issue 3, pp 289–304

A Large Subgraph of the Minimum Weight Triangulation

Authors

  • M. T. Dickerson
    • Department of Mathematics and Computer Science, Middlebury College, Middlebury, VT 05753-6145, USA dickerso@middlebury.edu
  • J. M. Keil
    • Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada keil@cs.usask.ca
  • M. H. Montague
    • Department of Mathematics and Computer Science, Middlebury College, Middlebury, VT 05753-6145, USA dickerso@middlebury.edu

DOI: 10.1007/PL00009320

Cite this article as:
Dickerson, M., Keil, J. & Montague, M. Discrete Comput Geom (1997) 18: 289. doi:10.1007/PL00009320

Abstract.

We present an O(n4)-time and O(n2)-space algorithm that computes a subgraph of the minimum weight triangulation (MWT) of a general point set. The algorithm works by finding a collection of edges guaranteed to be in any locally minimal triangulation. We call this subgraph the LMT-skeleton. We also give a variant called the modifiedLMT-skeleton that is both a more complete subgraph of the MWT and is faster to compute requiring only O(n2) time and O(n) space in the expected case for uniform distributions. Several experimental implementations of both approaches have shown that for moderate-sized point sets (up to 350 points^1) the skeletons are connected, enabling an efficient completion of the exact MWT. We are thus able to compute the MWT of substantially larger random point sets than have previously been computed.

^1Though in this paper we summarize some empirical findings for input sets of up to 350 points, a variant of the algorithm has been implemented and tested on up to 40,000 points producing connected subgraphs [2].

Copyright information

© 1997 Springer-Verlag New York Inc.