Locality-Aware Laplacian Mesh Smoothing

TL;DR

This paper introduces a simple reordering scheme for Laplacian Mesh Smoothing that significantly reduces cache misses and improves execution speed, achieving up to 75x speedup on multi-core systems.

Contribution

We propose a novel vertex reordering method based on reuse distance patterns to optimize cache performance in Laplacian Mesh Smoothing.

Findings

Achieved 75x speedup on 32 cores with reordering.

Reduced cache misses to near minimum levels.

Improved execution time by 32% over existing reordering methods.

Abstract

In this paper, we propose a novel reordering scheme to improve the performance of a Laplacian Mesh Smoothing (LMS). While the Laplacian smoothing algorithm is well optimized and studied, we show how a simple reordering of the vertices of the mesh can greatly improve the execution time of the smoothing algorithm. The idea of our reordering is based on (i) the postulate that cache misses are a very time consuming part of the execution of LMS, and (ii) the study of the reuse distance patterns of various executions of the LMS algorithm. Our reordering algorithm is very simple but allows for huge performance improvement. We ran it on a Westmere-EX platform and obtained a speedup of 75 on 32 cores compared to the single core execution without reordering, and a gain in execution of 32% on 32 cores compared to state of the art reordering. Finally, we show that we leave little room for a better ordering by reducing the L2 and L3 cache misses to a bare minimum.