  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.
