Layout of random circulant graphs

A circulant graph G is a graph on n vertices that can be numbered from 0 to n−1 in such a way that, if two vertices x and (x+d) mod n are adjacent, then every two vertices z and (z+d) mod n are adjacent. We call layout of the circulant graph any numbering that witness this definition. A random circulant graph results from deleting each edge of G uniformly with probability 1−p. We address the problem of finding the layout of a random circulant graph. We provide a polynomial time algorithm that approximates the solution and we bound the error of the approximation with high probability.