On integer network synthesis problem with tree-metric cost

Abstract

Network synthesis problem (NSP) asks to find a minimum-cost network satisfying a given connectivity requirement. Hau, Hirai, and Tsuchimura presented a simple greedy algorithm finding a half-integral optimal solution when the edge-cost is a tree metric. This generalizes the classical result by Gomory and Hu. 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 INSP is solvable in polynomial time when the edge-cost is a tree metric and each connectivity requirement is at least 2.