On integer network synthesis problem with tree-metric cost
Optimization and Control
2017-06-27 v1
Abstract
Network synthesis problem (NSP) is the problem of designing a minimum-cost network (from the empty network) satisfying a given connectivity requirement. Hau, Hirai, and Tsuchimura showed that if the edge-cost is a tree metric, then a simple greedy-type algorithm solves NSP to obtain a half-integral optimal solution. This is a generalization of the classical result by Gomory and Hu for the uniform edge-cost. In this note, we present an integer version of Hau, Hirai, and Tsuchimura's result for integer network synthesis problem (INSP), where a required network must have an integer capacity. We prove that if each connectivity requirement is at least 2 and the edge-cost is a tree metrc, then INSP can be solved in polynomial time.
Cite
@article{arxiv.1706.08015,
title = {On integer network synthesis problem with tree-metric cost},
author = {Hiroshi Hirai and Masashi Nitta},
journal= {arXiv preprint arXiv:1706.08015},
year = {2017}
}