A 10-Approximation of the π/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 = π/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.
Euclidean spanning trees
approximation algorithms
bounded-angle visibility
Theory of computation~Computational geometry
Theory of computation~Approximation algorithms analysis
13:1-13:15
Regular Paper
Ahmad
Biniaz
Ahmad Biniaz
School of Computer Science, University of Windsor, Canada
supported by NSERC.
Majid
Daliri
Majid Daliri
School of Electrical and Computer Engineering, University of Tehran, Iran
Amir Hossein
Moradpour
Amir Hossein Moradpour
School of Electrical and Computer Engineering, University of Tehran, Iran
10.4230/LIPIcs.STACS.2022.13
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Ahmad Biniaz, Majid Daliri, and Amir Hossein Moradpour
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