2010 International Symposium on Voronoi Diagrams in Science and Engineering (2006)

Banff Center, Calgary, Alberta, Canada

July 2, 2006 to July 5, 2006

ISBN: 0-7695-2630-6

pp: 54-59

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ISVD.2006.31

Y. Zhang , University of Texas at Dallas

S. Bereg , University of Texas at Dallas

M. L. Gavrilova , University of Calgary,Canada

ABSTRACT

We address the problemof robust point-locationin a generalized -dimensional Voronoi diagram. The exact point location requires the solution for expressions of degree four. A natural question is what can be done using expression of smaller degree. We apply polyhedral metrics for this task. In general dimensions two Minkowski metrics can be used L_1(Manhattan metric) and l_r00. The approximation factor is \sqrt d and the computation uses expressions of degree one. We also show that a polygonal metric can be applied in two dimensions. The compuation involves only calls of the algorithm ESSA for detecting the sign of a sum using floating-point arithmetic.

INDEX TERMS

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CITATION

Y. Zhang,
S. Bereg,
M. L. Gavrilova,
"Robust Point-Location in Generalized Voronoi Diagrams",

*2010 International Symposium on Voronoi Diagrams in Science and Engineering*, vol. 00, no. , pp. 54-59, 2006, doi:10.1109/ISVD.2006.31