Flowless: Extracting Densest Subgraphs Without Flow Computations

Abstract

The problem of finding dense components of a graph is a major primitive in graph mining and data analysis. The densest subgraph problem (DSP) that asks to find a subgraph with maximum average degree forms a basic primitive in dense subgraph discovery with applications ranging from community detection to unsupervised discovery of biological network modules [16]. The DSP is exactly solvable in polynomial time using maximum flows [14, 17, 22]. Due to the high computational cost of maximum flows, Charikar’s greedy approximation algorithm is usually preferred in practice due to its linear time and linear space complexity [3, 8]. It constitutes a key algorithmic idea in scalable solutions for large-scale dynamic graphs [5, 7]. However, its output density can be a factor 2 off the optimal solution.