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A simple greedy approximation algorithm for the unit disk cover problem | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 5، دوره 1، شماره 1، اردیبهشت 2020، صفحه 47-55 اصل مقاله (526.18 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2018.3044 | ||
| نویسندگان | ||
| Mahdi Imanparast؛ Seyed Naser Hashemi* | ||
| Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran | ||
| چکیده | ||
| Given a set $\mathcal P$ of $n$ points in the plane, the unit disk cover problem, which is known as an NP-hard problem, seeks to find the minimum number of unit disks that can cover all points of $\mathcal P$. We present a new $4$-approximation algorithm with running time $O(n \log n)$ for this problem. Our proposed algorithm uses a simple approach and is easy to understand and implement. | ||
| کلیدواژه‌ها | ||
| Computational geometry؛ Approximation algorithms؛ Unit disk cover problem؛ Facility location | ||
| مراجع | ||
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[7] P. Liu, D. Lu, A fast 25/6-approximation for the minimum unit disk cover problem, CoRR, abs/1406.3838, (2014).
[8] A. Biniaz, P. Liu, A. Maheshwari, M. Smid, Approximation algorithms for the unit disk cover problem in 2D and 3D, Computational Geometry: Theory and Applications, 60 (2017) 8-18.
[9] M. de Berg, O. Cheong, M. van Kreveld, M. Overmars, Computational Geometry: Algorithms and Applications, Springer Berlin Heidelberg, (2008) 95-115. | ||
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