Testability of minimum balanced multiway cut densities

TL;DR

This paper investigates the testability of balanced minimum multiway cut densities in weighted graphs, applying quadratic programming for approximation, and explores their connections to cluster analysis, statistical physics, and graph sequence convergence.

Contribution

It proves the testability of certain balanced minimum multiway cut densities and applies quadratic programming techniques for their approximation.

Findings

Certain balanced minimum multiway cut densities are testable.

Quadratic programming can approximate these cut densities.

Discussion on convergence of noisy graph sequences.

Abstract

Testable weighted graph parameters and equivalent notions of testability are investigated based on papers of Laszlo Lovasz and coauthors. We prove that certain balanced minimum multiway cut densities are testable. Using this fact, quadratic programming techniques are applied to approximate some of these quantities. The problem is related to cluster analysis and statistical physics. Convergence of special noisy graph sequences is also discussed.