  It is required to find an optimal order of constructing the edges of a
network so as to minimize the sum of the weighted connection times of relevant
pairs of vertices. Construction can be performed anytime anywhere in the
network, with a fixed overall construction speed. The problem is strongly
NP-hard even on stars. We present polynomial algorithms for the problem on
trees with a fixed number of leaves, and on general networks with a fixed
number of relevant pairs.
