Communication-Efficient Deterministic Parallel Algorithms for Planar Point Location and 2d Voronoi Diagram

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(~) ~> O(1) local memory each, communicate through some arbitrary interconnection network. They axe communication-efficient since they require, respectively, O(1) and O(logp) communication steps and O( v ) local computation per step. Both algorithms require O(~) ---Y2(p) local memory. 1 I n t r o d u c t i o n High performance computing systems nowadays, be either multicomputers or networks of workstations, consist of a set of p state-of-the-art processors, each with considerable local memory, connected to some interconnection network. These systems are usually coarse grained, i.e. the size of each local memory is "considerably larger" than O(1). Recently, there has been a growing interest in coarse grained computational models [4, 7, 16] and the design of coarse grained algorithms [10, 5, 8, 6, 9]. The work on computational models has tended to be motivated by the observation that '~fast algorithms" for fine-grained models rarely translate to fast code running oil coarse grained machines. The BSP model ([16]) was proposed in order to benefit from slackness in the number of processors and memory mapping via hash functions to hide communication latency and provide for the efficient execution of fine grained PRAM algorithms on coarse grained hardware. Other coarse grained models focus more on utilizing existing sequential code and minimizing global communication operations. These include the Coarse Grained Multicomputer (CGM) from [7] used in this paper and to be described below. In this * 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.