An Application of Algebraic Topology to Multiprocessor System Science

Abstract

The goals of this paper are to provide an introduction to the field of mathematics known as Algebraic Topology, to build skills in that field; and to show how to apply them to the field of Computer Science. This paper explains basic concepts in both fields and then shows how to use them in the example of a simple distributed computing problem. In general, we will follow, read, and understand the paper "Algebraic topology and distributed computing: a primer" by Maurice Herlihy and Sergio Rajsbaum [HR). In particular, we will be looking at sirnplicial maps, chain maps, and acyclic carriers to help us find when necessary communication is impossible for some multiprocessor systems.