Illustration of Collapsible Graph Algorithm

Abstract

In this section we will present an example of how the collapsible graph algorithm works. Our illustration uses a short, simple code segment involving matrix operands, however the program graph of this code segment contains a shared node. A memory model is provided, from which meaningful cost functions for the program operations are derived. These cost functions are illustrated as tables indexed by the shapes of operands and results. We then go through a process of three graph reductions, eventually reducing the graph to a single node, and in the process finding a shape assignment for each matrix operand.