Maximum Flows in Parametric Graph Templates

TL;DR

This paper introduces a method to analyze maximum flows in parametric graph templates representing nested, repetitive execution graphs of parallel programs, enabling efficient data movement bounds without explicit graph instantiation.

Contribution

It develops structurally-parametric polynomial-time algorithms for maximum flow analysis in nested, repetitive graphs, reducing complexity in dataflow analysis of parallel programs.

Findings

Efficient maximum flow computation on parametric, nested graphs.

Memory and computational savings by avoiding explicit graph instantiation.

Enabling analysis of previously intractable graph-based dataflow problems.

Abstract

Execution graphs of parallel loop programs exhibit a nested, repeating structure. We show how such graphs that are the result of nested repetition can be represented by succinct parametric structures. This parametric graph template representation allows us to reason about the execution graph of a parallel program at a cost that only depends on the program size. We develop structurally-parametric polynomial-time algorithm variants of maximum flows. When the graph models a parallel loop program, the maximum flow provides a bound on the data movement during an execution of the program. By reasoning about the structure of the repeating subgraphs, we avoid explicit construction of the instantiation (e.g., the execution graph), potentially saving an exponential amount of memory and computation. Hence, our approach enables graph-based dataflow analysis in previously intractable settings.