We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations in a normed space and with associated flow demands. The network may contain any finite number of additional unprescribed nodes from the space; these are known as the Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characterise the local topological structure of Steiner points in MGAs, showing, in particular, that for a wide range of metrics, and for some typical real-world cost-functions, the degree of each Steiner point is 3.
@article{arxiv.0909.4270,
title = {The Gilbert Arborescence Problem},
author = {M. G. Volz and M. Brazil and C. J. Ras and K. J. Swanepoel and D. A. Thomas},
journal= {arXiv preprint arXiv:0909.4270},
year = {2015}
}
Comments
19 pages, 7 figures. arXiv admin note: text overlap with arXiv:0903.2124