Cache-miss explanation for PR speedups

Establish whether processing one supernode at a time with a reduced-space data structure in the partition refinement (PR) reordering implementation reduces cache misses and thereby explains the large observed reductions in runtime relative to the original PR implementation of Jacquelin, Ng, and Peyton (2018).

Background

The paper introduces a reorganized implementation of the partition refinement (PR) method that processes and completely refines one supernode at a time, replacing an earlier implementation that refined partitions for all supernodes simultaneously.

This new implementation drastically reduces working storage (from many n-vectors to one n-vector plus a small number of N- and m'-vectors) and yields large runtime reductions in practice. The authors conjecture that fewer cache misses due to the smaller, more localized data structure are the likely cause of these runtime gains, but this causal explanation has not been established.