{"status":"public","page":"1 - 20","oa":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"acknowledgement":"We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy for some useful comments and remarks, and especially Thom Sulanke for modifying surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant DMS-1400876 and by the RFBR Grant 15-01-99563. Anton V. Nikitenko was supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government Grant 11.G34.31.0026.","month":"01","date_created":"2018-12-11T11:50:48Z","citation":{"apa":"Musin, O., &#38; Nikitenko, A. (2016). Optimal packings of congruent circles on a square flat torus. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-015-9742-6\">https://doi.org/10.1007/s00454-015-9742-6</a>","chicago":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00454-015-9742-6\">https://doi.org/10.1007/s00454-015-9742-6</a>.","ista":"Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square flat torus. Discrete &#38; Computational Geometry. 55(1), 1–20.","ieee":"O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square flat torus,” <i>Discrete &#38; Computational Geometry</i>, vol. 55, no. 1. Springer, pp. 1–20, 2016.","short":"O. Musin, A. Nikitenko, Discrete &#38; Computational Geometry 55 (2016) 1–20.","mla":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” <i>Discrete &#38; Computational Geometry</i>, vol. 55, no. 1, Springer, 2016, pp. 1–20, doi:<a href=\"https://doi.org/10.1007/s00454-015-9742-6\">10.1007/s00454-015-9742-6</a>.","ama":"Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat torus. <i>Discrete &#38; Computational Geometry</i>. 2016;55(1):1-20. doi:<a href=\"https://doi.org/10.1007/s00454-015-9742-6\">10.1007/s00454-015-9742-6</a>"},"_id":"1222","author":[{"full_name":"Musin, Oleg","first_name":"Oleg","last_name":"Musin"},{"first_name":"Anton","full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko"}],"doi":"10.1007/s00454-015-9742-6","abstract":[{"text":"We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason—the problem of “super resolution of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly, for the case N=7 there are three different optimal arrangements. Our proof is based on a computer enumeration of toroidal irreducible contact graphs.","lang":"eng"}],"publication":"Discrete & Computational Geometry","publication_status":"published","type":"journal_article","date_updated":"2021-01-12T06:49:11Z","volume":55,"day":"01","publisher":"Springer","year":"2016","date_published":"2016-01-01T00:00:00Z","scopus_import":1,"quality_controlled":"1","title":"Optimal packings of congruent circles on a square flat torus","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1212.0649"}],"oa_version":"Preprint","issue":"1","publist_id":"6111","language":[{"iso":"eng"}],"intvolume":"        55"}