A 10-Approximation of the pi/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 α, an α-spanning tree (α-ST) is a spanning tree of the complete Euclidean graph on P with the property that all edges incident to each point p ∈ P lie in a wedge of angle α centered at p. The α-minimum spanning tree (α-MST) problem asks for an α-ST of minimum total edge length. The seminal work of Anscher and Katz (ICALP 2014) shows the NP-hardness of the α-MST problem for α = 2π 3 , π and presents approximation algorithms for α = π 2 , 2π 3 , π. In this paper we study the α-MST problem for α = π2 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. 2012 ACM Subject Classification Theory of computation → Computational geometry; Theory of computation → Approximation algorithms analysis