As Internet technologies for long-distance transmission fall in price, and the volume of data transmission surpasses that of voice transmission, networks developed solely for the Internet are becoming the trend. However, long-distance Internet technologies add considerable delay to the signal...

The network design problem with relays (NDPR) is defined on an undirected graph G = (V, E, K), where V = {1, … , n} is a vertex set, E = {(i, j) : i, j ∈ V, i j} is an edge set. The set K = {(o(k), d(k))} is a set of communication pairs (or commodities): o(k) ∈ V and d(k) ∈ V denote the...