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A 10-Approximation of the π/2-MST

Authors Ahmad Biniaz, Majid Daliri, Amir Hossein Moradpour

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Author Details

Ahmad Biniaz
  • School of Computer Science, University of Windsor, Canada
Majid Daliri
  • School of Electrical and Computer Engineering, University of Tehran, Iran
Amir Hossein Moradpour
  • School of Electrical and Computer Engineering, University of Tehran, Iran

Funding

  • Biniaz, Ahmad: supported by NSERC.

Cite As Get BibTex

Ahmad Biniaz, Majid Daliri, and Amir Hossein Moradpour. A 10-Approximation of the π/2-MST. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.STACS.2022.13

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Euclidean spanning trees
  • approximation algorithms
  • bounded-angle visibility

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