Relaxation-based coarsening and multiscale graph organization

TL;DR

This paper introduces a new relaxation-based measure for graph coarsening that improves multiscale graph organization and optimization, with efficient computation and applications to combinatorial problems.

Contribution

It presents a novel relaxation-based closeness measure for graph coarsening, enhancing multiscale graph organization and optimization techniques.

Findings

The measure is linear in the number of edges.

Effective in multiscale methods for combinatorial optimization.

Demonstrates improved graph organization and problem solving.

Abstract

In this paper we generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the "closeness" between two nodes. The calculation of the measure is linear in the number of edges in the graph and involves just a small number of relaxation sweeps. A similar notion of distance is then calculated and used at each coarser level. We demonstrate the use of this measure in multiscale methods for several important combinatorial optimization problems and discuss the multiscale graph organization.