Finding Many Sparse Cuts Using Entropy Maximization

TL;DR

This paper introduces a novel randomized algorithm for identifying sparse cuts in graphs using entropy maximization and a dual Markov chain, offering new insights into graph clustering and sparsification.

Contribution

It presents a new entropy-based methodology and dual Markov chain approach for finding sparse cuts and graph sparsification, advancing existing graph clustering techniques.

Findings

The dual Markov chain process measures graph connectedness and mixing.

Entropy maximization offers a new perspective on sparse cuts.

Algorithms improve understanding of graph sparsification and clustering.

Abstract

A randomized algorithm for finding sparse cuts is given which is based on constructing a dual markov chain called multiscale rings process(MRP) and a new concept of entropy. It is shown how the time to absorption of the dual process measures the connectedness of the graph and mixing of the corresponding markov process which is then utilized to do clustering. The second algorithm uses the entropy which provides a new methodology and a set of tools to think about sparse cuts as well as sparsification of a graph.