A New Dynamic Algorithm for Densest Subhypergraphs

Abstract

Computing a dense subgraph is a fundamental problem in graph mining, with a diverse set of applications ranging from electronic commerce to community detection in social networks. In many of these applications, the underlying context is better modelled as a weighted hypergraph that keeps evolving with time.This motivates the problem of maintaining the densest subhypergraph of a weighted hypergraph in a dynamic setting, where the input keeps changing via a sequence of updates (hyperedge insertions/deletions). Previously, the only known algorithm for this problem was due to Hu et al. [HWC17]. This algorithm worked only on unweighted hypergraphs, and had an approximation ratio of (1 + )r 2 and an update time of O(poly(r, log n)), where r denotes the maximum rank of the input across all the updates.We obtain a new algorithm for this problem, which works even when the input hypergraph is weighted. Our algorithm has a significantly improved (near-optimal) approximation ratio of (1 + ) that is independent of r, and a similar update time of O(poly(r, log n)). It is the first (1 + )-approximation algorithm even for the special case of weighted simple graphs.To complement our theoretical analysis, we perform experiments with our dynamic algorithm on large-scale, real-world data-sets. Our algorithm significantly outperforms the state of the art [HWC17] both in terms of accuracy and efficiency.