On integer network synthesis problem with tree-metric cost

Hiroshi Hirai; Masashi Nitta

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arXiv · 1706.08015

On integer network synthesis problem with tree-metric cost

Hiroshi Hirai·Masashi Nitta

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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.

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Hiroshi Hirai, Masashi Nitta. 2017-06-25. On integer network synthesis problem with tree-metric cost. https://arxiv.org/abs/1706.08015

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