Preprocessing Imprecise Points and Splitting Triangulations

Authors:
Marc Kreveld;Maarten Löffler;Joseph S. Mitchell
Affiliations:
Department of Information and Computing Sciences, Utrecht University, The Netherlands;Department of Information and Computing Sciences, Utrecht University, The Netherlands;Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, USA
Venue:
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Year:
2008

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Abstract

Given a triangulation of a set of n points in the plane, each colored red or blue, we show how to compute a triangulation of just the blue points in time O(n). We apply this result to show that one can preprocess a set of disjoint regions (representing "imprecise points") in the plane having total complexity n in O(n logn) time so that if one point per region is specified with precise coordinates, a triangulation of the n points can be computed in O(n) time.