A PTAS for the metric case of the minimum sum-requirement communication spanning tree problem

This work considers the metric case of the minimum sum-requirement communication spanning tree problem (SROCT), which is an NP-hard particular case of the minimum communication spanning tree problem (OCT). Given an undirected graph G=(V,E) with non-negative lengths ω(e) associated to the edges satisfying the triangular inequality and non-negative routing weights r(u) associated to nodes u∈V, the objective is to find a spanning tree T of G, that minimizes: 12∑u∈V∑v∈V(r(u)+r(v))d(T,u,v), where d(H,x,y) is the minimum distance between nodes x and y in a graph H⊆G. We present a polynomial approximation scheme for the metric case of the SROCT  improving the until now best existing approximation algorithm for this problem.