An improved parallel algorithm for construction Voronoi diagram on a mesh-connected computer

While constructing a Voronoi diagram V_p for a set P of n points on a mesh-connected computer(MCC), it is necessary to find a set B of edges which are intersected by the dividing chain C during the merge process of two Voronoi diagrams V_L and V_A, where L and R contain the leftmost [n/2] points and the rightmost [n/2] points of P respectively. The computation of B requires two operations: First decide for each edge e in V_L and V_R whether its end vertices are closer to L or R, and then from that information, determine, whether e is intersected by C. The paper shows that the latter operation can be done in O(1) time without executing planar point location and the former operation can be executed without the computation of convex hulls. Therefore, the computation of B is reduced to only one planar point location