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Experimental Mathematics Volume 9, 2000 - Issue 2
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Original Articles

Conjecturally Optimal Coverings of an Equilateral Triangle with Up to 36 Equal Circles

Kari J. Nurmela Department of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, FIN-02015 HUT, Finland E-mail: [email protected]
Pages 241-250 | Published online: 04 Apr 2012

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Yu.G. Stoyan & V.M. Patsuk. (2014) Covering a convex 3D polytope by a minimal number of congruent spheres. International Journal of Computer Mathematics 91:9, pages 2010-2020.
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Articles from other publishers (21)

Ernesto G. Birgin, John L. Gardenghi & Antoine Laurain. (2023) Bounds on the Optimal Radius When Covering a Set with Minimum Radius Identical Disks. Mathematics of Operations Research.
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Ernesto G. Birgin, Antoine Laurain, Rafael Massambone & Arthur G. Santana. (2022) A Shape-Newton Approach to the Problem of Covering with Identical Balls. SIAM Journal on Scientific Computing 44:2, pages A798-A824.
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Alexander V. Khorkov & Shamil I. Galiev. (2021) Optimization of a k-covering of a bounded set with circles of two given radii. Open Computer Science 11:1, pages 232-240.
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E. G. Birgin, A. Laurain, R. Massambone & A. G. Santana. (2021) A Shape Optimization Approach to the Problem of Covering a Two-Dimensional Region with Minimum-Radius Identical Balls. SIAM Journal on Scientific Computing 43:3, pages A2047-A2078.
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Dirk Briskorn & Michael Dienstknecht. (2020) Covering polygons with discs: The problem of crane selection and location on construction sites. Omega 97, pages 102114.
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Plamen Petrov, Georgi Kostadinov, Petar Zhivkov, Veneta Velichkova, Stoyan Ivanov & Todor Balabanov. (2020) Multi-Objective Optimization in Image Approximation. Multi-Objective Optimization in Image Approximation.
Sh. I. Galiev & A. V. Khorkov. (2019) Optimization of the Number and Arrangement of Circles of Two Radii for Forming a k-Covering of a Bounded Set. Computational Mathematics and Mathematical Physics 59:4, pages 676-687.
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Sh. I. Galiev & A. V. Khorkov. (2019) On the Number and Arrangement of Sensors for the Multiple Covering of Bounded Plane Domains. Journal of Applied and Industrial Mathematics 13:1, pages 43-53.
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Alexander Kazakov, Anna Lempert & Quang Mung Le. 2019. Mathematical Optimization Theory and Operations Research. Mathematical Optimization Theory and Operations Research 195 206 .
Koushik Sinha, Sasthi C. Ghosh & Bhabani P. Sinha. 2016. Wireless Networks and Mobile Computing. Wireless Networks and Mobile Computing 356 369 .
Balázs Bánhelyi, Endre Palatinus & Balázs L. Lévai. (2014) Optimal circle covering problems and their applications. Central European Journal of Operations Research 23:4, pages 815-832.
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Koushik Sinha, Sasthi Ghosh & Bhabani Sinha. 2015. Wireless Networks and Mobile Computing. Wireless Networks and Mobile Computing 335 348 .
S. Seriani, P. Gallina & A. Gasparetto. (2014) A Performance Index for Planar Repetitive Workspace Robots. Journal of Mechanisms and Robotics 6:3.
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Chuanming Zong. (2014) Packing, covering and tiling in two-dimensional spaces. Expositiones Mathematicae 32:4, pages 297-364.
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HIROFUMI AOTA, TAKURO FUKUNAGA & HIROSHI NAGAMOCHI. (2012) AN APPROXIMATION ALGORITHM FOR LOCATING MAXIMAL DISKS WITHIN CONVEX POLYGONS. International Journal of Computational Geometry & Applications 21:06, pages 661-684.
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Wei-Chieh Ke, Bing-Hong Liu & Ming-Jer Tsai. (2011) The critical-square-grid coverage problem in wireless sensor networks is NP-Complete. Computer Networks 55:9, pages 2209-2220.
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Wei-Chieh Ke, Bing-Hong Liu & Ming-Jer Tsai. (2011) Efficient Algorithm for Constructing Minimum Size Wireless Sensor Networks to Fully Cover Critical Square Grids. IEEE Transactions on Wireless Communications 10:4, pages 1154-1164.
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Y. G. Stoyan & V. M. Patsuk. (2008) Covering a compact polygonal set by identical circles. Computational Optimization and Applications 46:1, pages 75-92.
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Sh. I. Galiev & M. A. Karpova. (2010) Optimization of multiple covering of a bounded set with circles. Computational Mathematics and Mathematical Physics 50:4, pages 721-732.
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Gautam K. Das, Sandip Das, Subhas C. Nandy & Bhabani P. Sinha. (2006) Efficient algorithm for placing a given number of base stations to cover a convex region. Journal of Parallel and Distributed Computing 66:11, pages 1353-1358.
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Gautam K. Das, Sandip Das, Subhas C. Nandy & Bhabani P. Sinha. 2005. Distributed Computing – IWDC 2005. Distributed Computing – IWDC 2005 57 62 .

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