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A 10-Approximation of the π/2-MST

Authors Ahmad Biniaz, Majid Daliri, Amir Hossein Moradpour

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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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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.

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

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.

References

  1. Eyal Ackerman, Tsachik Gelander, and Rom Pinchasi. Ice-creams and wedge graphs. Computational Geometry: Theory and Applications, 46(3):213-218, 2013. Google Scholar
  2. Oswin Aichholzer, Thomas Hackl, Michael Hoffmann, Clemens Huemer, Attila Pór, Francisco Santos, Bettina Speckmann, and Birgit Vogtenhuber. Maximizing maximal angles for plane straight-line graphs. Computational Geometry: Theory and Applications, 46(1):17-28, 2013. Also in WADS'07. Google Scholar
  3. Rom Aschner and Matthew J. Katz. Bounded-angle spanning tree: Modeling networks with angular constraints. Algorithmica, 77(2):349-373, 2017. Also in ICALP'14. Google Scholar
  4. Rom Aschner, Matthew J. Katz, and Gila Morgenstern. Do directional antennas facilitate in reducing interferences? In Proceedings of the 13th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT), pages 201-212, 2012. Google Scholar
  5. Rom Aschner, Matthew J. Katz, and Gila Morgenstern. Symmetric connectivity with directional antennas. Computational Geometry: Theory and Applications, 46(9):1017-1026, 2013. Also in ALGOSENSORS'12. Google Scholar
  6. Stav Ashur and Matthew J. Katz. A 4-approximation of the 2π/3-MST. In Proceedings of the 17th Algorithms and Data Structures Symposium (WADS), 2021. Google Scholar
  7. Ahmad Biniaz. Euclidean bottleneck bounded-degree spanning tree ratios. Discrete & Computational Geometry, https://doi.org/10.1007/s00454-021-00286-4, 2021. Also in SODA'20. Google Scholar
  8. Ahmad Biniaz, Prosenjit Bose, Anna Lubiw, and Anil Maheshwari. Bounded-Angle Minimum Spanning Trees. In Proceedings of the 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020), pages 14:1-14:22, 2020. Google Scholar
  9. Prosenjit Bose, Paz Carmi, Mirela Damian, Robin Y. Flatland, Matthew J. Katz, and Anil Maheshwari. Switching to directional antennas with constant increase in radius and hop distance. Algorithmica, 69(2):397-409, 2014. Also in WADS'11. Google Scholar
  10. Ioannis Caragiannis, Christos Kaklamanis, Evangelos Kranakis, Danny Krizanc, and Andreas Wiese. Communication in wireless networks with directional antennas. In Proceedings of the 20th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 344-351, 2008. Google Scholar
  11. Paz Carmi, Matthew J. Katz, Zvi Lotker, and Adi Rosén. Connectivity guarantees for wireless networks with directional antennas. Computational Geometry: Theory and Applications, 44(9):477-485, 2011. Google Scholar
  12. Timothy M. Chan. Euclidean bounded-degree spanning tree ratios. Discrete & Computational Geometry, 32(2):177-194, 2004. Also in SoCG'03. Google Scholar
  13. Mirela Damian and Robin Y. Flatland. Spanning properties of graphs induced by directional antennas. Discrete Mathematics, Algorithms and Applications, 5(3), 2013. Google Scholar
  14. Stefan Dobrev, Evangelos Kranakis, Danny Krizanc, Jaroslav Opatrny, Oscar Morales Ponce, and Ladislav Stacho. Strong connectivity in sensor networks with given number of directional antennae of bounded angle. Discrete Mathematics, Algorithms and Applications, 4(3), 2012. Also in COCOA'10. Google Scholar
  15. Stefan Dobrev, Evangelos Kranakis, Oscar Morales Ponce, and Milan Plzík. Robust sensor range for constructing strongly connected spanning digraphs in UDGs. In Proceedings of the 7th International Computer Science Symposium in Russia (CSR), pages 112-124, 2012. Google Scholar
  16. Adrian Dumitrescu, János Pach, and Géza Tóth. Drawing Hamiltonian cycles with no large angles. Electronic Journal of Combinatorics, 19(2):P31, 2012. Also in GD'94. Google Scholar
  17. Sándor P. Fekete, Samir Khuller, Monika Klemmstein, Balaji Raghavachari, and Neal E. Young. A network-flow technique for finding low-weight bounded-degree spanning trees. Journal of Algorithms, 24(2):310-324, 1997. Also in IPCO 1996. Google Scholar
  18. Sándor P. Fekete and Gerhard J. Woeginger. Angle-restricted tours in the plane. Computational Geometry: Theory and Applications, 8:195-218, 1997. Google Scholar
  19. Raja Jothi and Balaji Raghavachari. Degree-bounded minimum spanning trees. Discrete Applied Mathematics, 157(5):960-970, 2009. Google Scholar
  20. Samir Khuller, Balaji Raghavachari, and Neal E. Young. Low-degree spanning trees of small weight. SIAM Journal on Computing, 25(2):355-368, 1996. Also in STOC'94. Google Scholar
  21. Evangelos Kranakis, Fraser MacQuarrie, and Oscar Morales Ponce. Connectivity and stretch factor trade-offs in wireless sensor networks with directional antennae. Theoretical Computer Science, 590:55-72, 2015. Google Scholar
  22. Clyde L. Monma and Subhash Suri. Transitions in geometric minimum spanning trees. Discrete & Computational Geometry, 8:265-293, 1992. Also in SoCG'91. Google Scholar
  23. Tien Tran, Min Kyung An, and Dung T. Huynh. Antenna orientation and range assignment algorithms in directional WSNs. IEEE/ACM Transaction on Networking, 25(6):3368-3381, 2017. Also in INFOCOM'16. Google Scholar
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