Spectral partitioning of graphs into compact, connected regions

TL;DR

This paper introduces SpecReCom, a spectral algorithm for partitioning graphs into connected, balanced regions, demonstrating its effectiveness in producing more compact partitions than existing methods on grid and planar graphs.

Contribution

The paper presents a novel spectral recombination algorithm, SpecReCom, with a balanced variant, BalSpecReCom, for graph partitioning into connected, compact, and balanced regions.

Findings

SpecReCom outperforms RevReCom in producing compact partitions.

The algorithms effectively handle constraints like balanced region sizes.

Empirical tests on grid and planar graphs validate the approach.

Abstract

We define and study a spectral recombination algorithm, SpecReCom, for partitioning a graph into a given number of connected parts. It is straightforward to introduce additional constraints such as the requirement that the weight (or number of vertices) in each part is approximately balanced, and we exemplify this by stating a variant, BalSpecReCom, of the SpecReCom algorithm. We provide empirical evidence that the algorithm achieves more compact partitions than alternatives such as RevReCom by studying a $56\times 56$ grid graph and a planar graph obtained from the state of Colorado.