Robust Point-Location in Generalized Voronoi Diagrams

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 L_infin. 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.