Communication-efficient deterministic parallel algorithms for planar point location and 2d Voronoi Diagram

Abstract

In this paper we describe deterministic parallel algorithms for planar point location and for building the Voronoi Diagram of n co-planar points. These algorithms are designed for BSP-like models of computation, where p processors, with $O\left( {\tfrac{n}{p}} \right)$ ≫ O(1) local memory each, communicate through some arbitrary interconnection network. They are communication-efficient since they require, respectively, O(1) and O(log p) communication steps and $O\left( {\tfrac{{n \log n}}{p}} \right)$ local computation per step. Both algorithms require $O\left( {\tfrac{n}{p}} \right)$ = Ω(p) local memory.

Partially supported by NSERC

Part of this work was done while the second author was with the LIP at the ENS Lyon and while the authors visited each other in Lyon and in Halifax. Support from the respective Institutions is acknowledged.