Advanced Coarsening Schemes for Graph Partitioning

TL;DR

This paper explores advanced coarsening schemes in multilevel graph partitioning, comparing various methods to improve efficiency and quality in large-scale graph problems.

Contribution

It introduces and evaluates novel coarsening strategies, emphasizing the importance of the coarsening phase in multilevel graph partitioning frameworks.

Findings

Matching-based coarsening improves partition quality.

Algebraic distance enhances coarsening efficiency.

Certain schemes reduce running time significantly.

Abstract

The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on large-scale graphs. Most of the attention in designing the multilevel partitioning frameworks has been on the refinement phase. In this work we focus on the coarsening phase, which is responsible for creating structurally similar to the original but smaller graphs. We compare different matching- and AMG-based coarsening schemes, experiment with the algebraic distance between nodes, and demonstrate computational results on several classes of graphs that emphasize the running time and quality advantages of different coarsenings.