A PTAS for the Metric Case of the Minimum Sum-Requirement Communication Spanning Tree Problem

Abstract

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: $\frac{1}{2}\sum_{u\in V}\sum_{v\in V}\left(r(u)+r(v)\right)d(T,u,v)$, 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.