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

In this paper, we reduce the complexity of approximating the correlation clustering problem from O(m×left( 2+ α (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 α(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×α(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.