Chapter 4 - Deterministic Parallel Computational Geometry

Abstract

This chapter describes the general methods used for designing deterministic parallel algorithms in computational geometry. The techniques for shared-memory parallel machines are also discussed. In parallel computational geometry, it is a rule that the known sequential techniques do not translate well into a parallel setting. The difficulty is usually that these techniques use methods that either seem to be inherently sequential, or would result in inefficient parallel implementations. Thus, new paradigms are needed for parallel computational geometry. Cascading is a sampling and iterative refinement method for the sorting problem and for the solutions of geometric problems. The parallel random access machine (PRAM) is the main vehicle used to study the parallel algorithmics of geometric problems. The PRAM model of parallel computation is the shared-memory model in which the processors operate synchronously. The Concurrent Read Exclusive Write (CREW)) version of this model allows many processors to simultaneously read the content of a memory location, but forbids any two processors from simultaneously attempting to write in the same memory location (even if they are trying to write the same thing).