Single-Source Dilation-Bounded Minimum Spanning Trees

Abstract

Given a set S of points in the plane, a geometric network for S is a graph G with vertex set S and straight edges. We consider a broadcasting situation, where one point r ∈ S is a designated source. Given a dilation factor δ, we ask for a geometric network G such that for every point v ∈ S there is a path from r to v in G of length at most δ|rv|, and such that the total edge length is minimized. We show that finding such a network of minimum total edge length is NP-hard, and give an approximation algorithm.