On Near Optimal Spectral Expander Graphs of Fixed Size

TL;DR

This paper introduces heuristic algorithms, including a novel Metropolis Coupled Simulated Annealer, to generate and optimize fixed-size regular graphs with near-optimal spectral expansion properties.

Contribution

The paper presents a new heuristic approach and a specialized optimization algorithm for constructing near-optimal spectral expander graphs of fixed size.

Findings

Successfully generates regular graphs with improved spectral gaps

Introduces MCSA for spectral gap optimization in fixed-size graphs

Provides practical methods for designing spectral expanders

Abstract

We present a pair of heuristic algorithms. The first is to generate a random regular graph of fixed size. The second is the introduction of the Metropolis Coupled Simulated Annealer (MCSA) for optimizing spectral gaps in fixed size regular graphs.