A polynomial time approximation scheme for embedding a directed hypergraph on a ring

We study the problem of embedding a directed hypergraph on a ring that has applications in optical network communications. The undirected version (MCHEC) has been extensively studied. It was shown that the undirect version was NP-complete. A polynomial time approximation scheme (PTAS) for the undirected version has been developed. In this paper, we design a polynomial time approximation scheme for the directed version.