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

• Published in: Discrete Applied Mathematics Vol. 228; pp. 158 - 175
• Main Authors: Ravelo, S.V., Ferreira, C.E.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 10.09.2017; Elsevier BV
• Subjects: Algorithms; Approximation; Communication spanning tree problem; Graphs; Mathematical analysis; Metric problem; Polynomial approximation scheme; Polynomials; Communication spanning tree problem; Metric problem; Polynomial approximation scheme
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/j.dam.2016.09.031

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.