In network theory, the problem of simulating one architecture into another architecture is converted into a graph embedding problem. In this paper, we have extended our work in [1] and give algorithms to compute optimal edge-congestion of embedding hypercubes, folded hypercubes, crossed cubes and circulant networks into hypertrees thereby proving that the edge-congestion bound obtained in [1] is sharp. © 2019 NSP Natural Sciences Publishing Cor.