Faster Approximation Algorithms for Parameterized Graph Clustering and Edge Labeling

TL;DR

This paper introduces faster, scalable approximation algorithms for the NP-hard LambdaCC graph clustering problem, generalizing several objectives and including a new edge labeling problem relevant to social networks.

Contribution

It presents the first fast, combinatorial approximation algorithms for LambdaCC and introduces a novel parameterized edge labeling problem with broad applicability.

Findings

Algorithms are orders of magnitude faster than previous methods.

Provides a posteriori guarantees for existing heuristics.

Introduces a new edge labeling problem of independent interest.

Abstract

Graph clustering is a fundamental task in network analysis where the goal is to detect sets of nodes that are well-connected to each other but sparsely connected to the rest of the graph. We present faster approximation algorithms for an NP-hard parameterized clustering framework called LambdaCC, which is governed by a tunable resolution parameter and generalizes many other clustering objectives such as modularity, sparsest cut, and cluster deletion. Previous LambdaCC algorithms are either heuristics with no approximation guarantees, or computationally expensive approximation algorithms. We provide fast new approximation algorithms that can be made purely combinatorial. These rely on a new parameterized edge labeling problem we introduce that generalizes previous edge labeling problems that are based on the principle of strong triadic closure and are of independent interest in social network analysis. Our methods are orders of magnitude more scalable than previous approximation algorithms and our lower bounds allow us to obtain a posteriori approximation guarantees for previous heuristics that have no approximation guarantees of their own.