Parallel coarsening of graph data with spectral guarantees

TL;DR

This paper introduces a parallel spectral coarsening algorithm for large graphs that preserves spectral properties while significantly reducing computational complexity and enabling scalable parallel processing.

Contribution

It develops a new spectral coarsening method with lower work complexity and parallelizability, improving scalability over existing approaches.

Findings

Algorithm achieves impressive scaling on meshes.

Reduces computational work compared to traditional methods.

Preserves spectral properties effectively.

Abstract

Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields is the preservation of spectral properties with regards to the original graph. While many methods exist to perform this task, they typically require expensive linear algebraic operations and yield high work complexities. We adapt a spectral coarsening bound from the literature in order to develop a coarsening algorithm with a work complexity that is drastically smaller than previous work. We further show that this algorithm is easily parallelizable and presents impressive scaling results on meshes.