PTAS’s for some metric p-source communication spanning tree problems

Abstract

In this work we consider some NP-hard cases of the metric p-source communication spanning tree problem (metric p-OCT). Given an undirected complete graph G = (V,E) with non-negative length ω(e) associated to each edge e ∈ E satisfying the triangular inequality, a set S ⊆ V of p vertices and non-negative routing requirements ψ(u, v) between all pairs of nodes u ∈ S and v ∈ V, themetric p-OCT’s objective is to find a spanning tree T ofG, thatminimizes:Σu∈SΣv∈V ψ(u, v)d(T, u, v), where d(H, x, y) is the minimumdistance between nodes x and y in a graph H ⊆ G. This problem is a particular case of the optimum communication spanning tree problem (OCT).We prove a general result which allows us to derive polynomial approximation schemes for someNP-hard cases of the metric p-OCT improving the existing ratios for these problems.