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We address the problem of robust point-location in a generalized d-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 L1 (Manhattan metric) and Linfin. The approximation factor is radic(d) and the computation uses expressions of degree one. We also show that a polygonal metric can be applied in two dimensions. The computation involves only 0(lg k) calls of the algorithm ESSA for detecting the sign of a sum using floating-point arithmetic.
Date of Conference: 2-5 July 2006