Efficient algorithm for large spectral partitions

TL;DR

This paper introduces an improved spectral partitioning algorithm that leverages density function representations and neighborhood restrictions to enhance computational efficiency, enabling large-scale 3D volumic spectral partition computations.

Contribution

The paper proposes a novel algorithm that reduces computational time for spectral partitioning by focusing on high-density regions, extending methods to 3D surfaces and volumic partitions.

Findings

Reduced computational time for spectral partitioning.

First large-scale volumic 3D spectral partition computations.

Enhanced algorithms for surfaces and 3D domains.

Abstract

We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by restricting the computation to neighbourhoods of regions where the associated densities are above a certain threshold. The algorithm extends and improves known methods in the plane and on surfaces in dimension 3. It also makes possible to make some of the first computations of volumic 3D spectral partitions on sufficiently large discretizations.