Balancing minimum spanning trees and multiple-source minimum routing cost spanning trees on metric graphs

Both the building cost and the multiple-source routing cost are important considerations in construction of a network system. A spanning tree with minimum building cost among all spanning trees is called a minimum spanning tree (MST), and a spanning tree with minimum k-source routing cost among all spanning trees is called a k-source minimum routing cost spanning tree (k-MRCT). This paper proposes an algorithm to construct a spanning tree T for a metric graph G with a source vertex set S such that the building cost of T is at most 1+2/(α−1) times of that of an MST of G, and the k-source routing cost of T is at most α(1+2(k−1)(n−2)/k(n+k−2)) times of that of a k-MRCT of G with respect to S, where α>1, k=|S| and n is the number of vertices of G.