Robust Densest Subgraph Discovery

TL;DR

This paper introduces a robust framework for densest subgraph discovery that accounts for uncertain edge weights using robust optimization and sampling oracles, with algorithms supported by strong theoretical guarantees and validated through experiments.

Contribution

It proposes a novel robust densest subgraph model under uncertain weights and develops algorithms with proven performance guarantees, extending traditional methods to real-world uncertain data.

Findings

Algorithms outperform baseline methods on synthetic and real-world graphs.

The proposed methods have strong theoretical performance guarantees.

Experimental results confirm effectiveness in uncertain weight scenarios.

Abstract

Dense subgraph discovery is an important primitive in graph mining, which has a wide variety of applications in diverse domains. In the densest subgraph problem, given an undirected graph $G=(V,E)$ with an edge-weight vector $w=(w_e)_{e\in E}$, we aim to find $S\subseteq V$ that maximizes the density, i.e., $w(S)/|S|$, where $w(S)$ is the sum of the weights of the edges in the subgraph induced by $S$. Although the densest subgraph problem is one of the most well-studied optimization problems for dense subgraph discovery, there is an implicit strong assumption; it is assumed that the weights of all the edges are known exactly as input. In real-world applications, there are often cases where we have only uncertain information of the edge weights. In this study, we provide a framework for dense subgraph discovery under the uncertainty of edge weights. Specifically, we address such an uncertainty issue using the theory of robust optimization. First, we formulate our fundamental problem, the robust densest subgraph problem, and present a simple algorithm. We then formulate the robust densest subgraph problem with sampling oracle that models dense subgraph discovery using an edge-weight sampling oracle, and present an algorithm with a strong theoretical performance guarantee. Computational experiments using both synthetic graphs and popular real-world graphs demonstrate the effectiveness of our proposed algorithms.