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.
@article{arxiv.2104.09312,
title = {Minimizing the total weighted pairwise connection time in network construction problems},
author = {Igor Averbakh},
journal= {arXiv preprint arXiv:2104.09312},
year = {2021}
}