Correlation Clustering Algorithm for Dynamic Complete Signed Graphs: An Index-based Approach

TL;DR

This paper introduces an efficient index-based correlation clustering algorithm for dynamic complete signed graphs, significantly reducing complexity and enabling real-time updates with proven effectiveness on real-world data.

Contribution

The authors develop a novel index-based approach that reduces approximation complexity from O(m×(2+α(G))) to O(m+n), facilitating dynamic graph updates.

Findings

Algorithm reduces processing time by 34% on average.

Supports dynamic updates like edge sign flipping and vertex changes.

Maintains the same output as the original algorithm.

Abstract

In this paper, we reduce the complexity of approximating the correlation clustering problem from $O(m\times\left( 2+ \alpha (G) \right)+n)$ to $O(m+n)$ for any given value of $\varepsilon$ for a complete signed graph with $n$ vertices and $m$ positive edges where $\alpha(G)$ is the arboricity of the graph. Our approach gives the same output as the original algorithm and makes it possible to implement the algorithm in a full dynamic setting where edge sign flipping and vertex addition/removal are allowed. Constructing this index costs $O(m)$ memory and $O(m\times\alpha(G))$ time. We also studied the structural properties of the non-agreement measure used in the approximation algorithm. The theoretical results are accompanied by a full set of experiments concerning seven real-world graphs. These results shows superiority of our index-based algorithm to the non-index one by a decrease of %34 in time on average.