Minimum-congestion hypergraph embedding in a cycle

The minimum-congestion hypergraph embedding in a cycle (MCHEC) problem is to embed the n edges in an m-vertex hypergraph as paths in a cycle on the same number of vertices, such that congestion-the maximum number of paths that use any single edge in the cycle-is minimized. The MCHEC problem has applications in electronic design automation and parallel computing. In this paper, it is proven that the MCHEC problem is NP-complete. An O((nm)^k+1) algorithm is described that computes an embedding with congestion k or determines that such an embedding does not exist. Finally, a linear-time approximation algorithm for arbitrary instances is presented that computes an embedding whose congestion is at most three times optimal