A 10-approximation of the 2-mst

Bounded-angle spanning trees of points in the plane have received considerable attention in the context of wireless networks with directional antennas. For a point set P in the plane and an angle alpha, an alpha-spanning tree (alpha-ST) is a spanning tree of the complete Euclidean graph on P with the property that all edges incident to each point p is an element of P lie in a wedge of angle alpha centered at p. The alpha-minimum spanning tree (alpha-MST) problem asks for an alpha-ST of minimum total edge length. The seminal work of Anscher and Katz (ICALP 2014) shows the NP-hardness of the alpha-MST problem for alpha = 2 pi 3 , n and presents approximation algorithms for alpha = pi 2 , 2 pi 3, n.In this paper we study the alpha-MST problem for alpha = pi 2 which is also known to be NP-hard. We present a 10-approximation algorithm for this problem. This improves the previous best known approximation ratio of 16.