On a Connection Between Small Set Expansions and Modularity Clustering in Social Networks

TL;DR

This paper establishes a link between small-set expansion problems in theoretical computer science and modularity clustering in social network analysis, showing that advances in one could impact the other.

Contribution

It reveals a novel connection between small-set expansion and modularity clustering, suggesting that algorithms for one could influence the other.

Findings

Sub-exponential algorithms for small-set expansion imply sub-exponential approximations for modularity clustering.

The connection highlights potential computational hardness implications across domains.

Provides a new perspective on the complexity of community detection in social networks.

Abstract

In this paper we explore a connection between two seemingly different problems from two different domains: the small-set expansion problem studied in unique games conjecture, and a popular community finding approach for social networks known as the modularity clustering approach. We show that a sub-exponential time algorithm for the small-set expansion problem leads to a sub-exponential time constant factor approximation for some hard input instances of the modularity clustering problem.