We will say that a clique graph H(V,E) has a -cluster structure, if the size of each clique in H is at least
.
For a fixed
we say that a randomized algorithm A reconstructs
-cluster structures w.h.p. if for each
there exists n0 such that for each
and for any graph
,
where H is clique graph with n vertices and
structure,
.
First we describe a theoretic algorithm which reconstructs -cluster structures w.h.p. The correctness proof of the algorithm will be outlined. We then present the practical heuristic, which is based on the theoretical algorithm and preserves most of its properties.