Boolean Set Operations on a MIMD Distributed Memory Machine

We present an efficient algorithm for Boolean Set operations between two arbitrary manifold polyhedra, on a MIMD distributed memory machine such as as the nCUBE2 or the Intel IPSC860. For two manifold polyhedra with O(n) edges each, our algorithms run in 0(log2 n ) time on an n 2 processor MIMD machine. Our model of computation assumes exact arithmetic on each processor and the ability for any processor PI to communicate an 0(1) size message in 0(1) time to any other processor P2 if PI knows P2'S ID. In this paper we also present a distributed data structure for arbitrary polyhedra on MIMD distributed memory machines.

[1]  Mikhail J. Atallah,et al.  Efficient Parallel Solutions to Geometric Problems , 1985, ICPP.

[2]  S. Lakshmivarahan,et al.  Parallel Sorting Algorithms , 1984, Adv. Comput..

[3]  Leonidas J. Guibas,et al.  Parallel computational geometry , 1988, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[4]  M. Karasick.  On the representation and manipulation of rigid solids , 1989 .

[5]  A.A.G. Requicha,et al.  Boolean operations in solid modeling: Boundary evaluation and merging algorithms , 1985, Proceedings of the IEEE.

[6]  Kenneth E. Batcher,et al.  Sorting networks and their applications , 1968, AFIPS Spring Joint Computing Conference.

[7]  Bruce F. Naylor,et al.  Set operations on polyhedra using binary space partitioning trees , 1987, SIGGRAPH.