Robust Point-Location in Generalized Voronoi Diagrams

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.