Cut Tree Construction from Massive Graphs

TL;DR

This paper introduces a new algorithm for constructing cut trees in large-scale graphs, significantly reducing computational time and enabling analysis of billion-scale networks.

Contribution

A novel cut-tree construction algorithm optimized for real-world large graphs, achieving orders of magnitude speedup over previous methods.

Findings

Algorithm is several orders of magnitude faster than existing methods.

Successfully constructs cut trees for billion-scale graphs.

Demonstrates practical applicability to large real-world networks.

Abstract

The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining, as they support various procedures related to the minimum cut, maximum flow, and connectivity. However, the crucial drawback with cut trees is the computational cost of their construction. In theory, a cut tree is built by applying a maximum flow algorithm for $n$ times, where $n$ is the number of vertices. Therefore, naive implementations of this approach result in cubic time complexity, which is obviously too slow for today's large-scale graphs. To address this issue, in the present study, we propose a new cut-tree construction algorithm tailored to real-world networks. Using a series of experiments, we demonstrate that the proposed algorithm is several orders of magnitude faster than previous algorithms and it can construct cut trees for billion-scale graphs.