{"publication_status":"published","intvolume":"      6570","title":"Covering and packing with spheres by diagonal distortion in R^n","publisher":"Springer","abstract":[{"lang":"eng","text":"We address the problem of covering ℝ n with congruent balls, while minimizing the number of balls that contain an average point. Considering the 1-parameter family of lattices defined by stretching or compressing the integer grid in diagonal direction, we give a closed formula for the covering density that depends on the distortion parameter. We observe that our family contains the thinnest lattice coverings in dimensions 2 to 5. We also consider the problem of packing congruent balls in ℝ n , for which we give a closed formula for the packing density as well. Again we observe that our family contains optimal configurations, this time densest packings in dimensions 2 and 3."}],"quality_controlled":"1","date_updated":"2021-01-12T07:52:15Z","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T12:05:13Z","date_published":"2011-05-03T00:00:00Z","language":[{"iso":"eng"}],"editor":[{"last_name":"Calude","first_name":"Cristian","full_name":"Calude, Cristian"},{"first_name":"Grzegorz","full_name":"Rozenberg, Grzegorz","last_name":"Rozenberg"},{"last_name":"Salomaa","full_name":"Salomaa, Arto","first_name":"Arto"}],"year":"2011","oa_version":"Submitted Version","month":"05","author":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"id":"36E4574A-F248-11E8-B48F-1D18A9856A87","last_name":"Kerber","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","first_name":"Michael"}],"pubrep_id":"539","day":"03","doi":"10.1007/978-3-642-19391-0_2","_id":"3796","file_date_updated":"2020-07-14T12:46:16Z","oa":1,"file":[{"content_type":"application/pdf","checksum":"aaf22b4d7bd4277ffe8db532119cf474","date_created":"2018-12-12T10:07:42Z","file_id":"4640","file_size":436875,"relation":"main_file","creator":"system","access_level":"open_access","file_name":"IST-2016-539-v1+1_2011-B-01-CoveringPacking.pdf","date_updated":"2020-07-14T12:46:16Z"}],"publication":"Rainbow of Computer Science","alternative_title":["LNCS"],"volume":6570,"citation":{"apa":"Edelsbrunner, H., &#38; Kerber, M. (2011). Covering and packing with spheres by diagonal distortion in R^n. In C. Calude, G. Rozenberg, &#38; A. Salomaa (Eds.), <i>Rainbow of Computer Science</i> (Vol. 6570, pp. 20–35). Springer. <a href=\"https://doi.org/10.1007/978-3-642-19391-0_2\">https://doi.org/10.1007/978-3-642-19391-0_2</a>","chicago":"Edelsbrunner, Herbert, and Michael Kerber. “Covering and Packing with Spheres by Diagonal Distortion in R^n.” In <i>Rainbow of Computer Science</i>, edited by Cristian Calude, Grzegorz Rozenberg, and Arto Salomaa, 6570:20–35. Dedicated to Hermann Maurer on the Occasion of His 70th Birthday. Springer, 2011. <a href=\"https://doi.org/10.1007/978-3-642-19391-0_2\">https://doi.org/10.1007/978-3-642-19391-0_2</a>.","short":"H. Edelsbrunner, M. Kerber, in:, C. Calude, G. Rozenberg, A. Salomaa (Eds.), Rainbow of Computer Science, Springer, 2011, pp. 20–35.","mla":"Edelsbrunner, Herbert, and Michael Kerber. “Covering and Packing with Spheres by Diagonal Distortion in R^n.” <i>Rainbow of Computer Science</i>, edited by Cristian Calude et al., vol. 6570, Springer, 2011, pp. 20–35, doi:<a href=\"https://doi.org/10.1007/978-3-642-19391-0_2\">10.1007/978-3-642-19391-0_2</a>.","ieee":"H. Edelsbrunner and M. Kerber, “Covering and packing with spheres by diagonal distortion in R^n,” in <i>Rainbow of Computer Science</i>, vol. 6570, C. Calude, G. Rozenberg, and A. Salomaa, Eds. Springer, 2011, pp. 20–35.","ama":"Edelsbrunner H, Kerber M. Covering and packing with spheres by diagonal distortion in R^n. In: Calude C, Rozenberg G, Salomaa A, eds. <i>Rainbow of Computer Science</i>. Vol 6570. Dedicated to Hermann Maurer on the Occasion of His 70th Birthday. Springer; 2011:20-35. doi:<a href=\"https://doi.org/10.1007/978-3-642-19391-0_2\">10.1007/978-3-642-19391-0_2</a>","ista":"Edelsbrunner H, Kerber M. 2011.Covering and packing with spheres by diagonal distortion in R^n. In: Rainbow of Computer Science. LNCS, vol. 6570, 20–35."},"page":"20 - 35","ddc":["000"],"series_title":"Dedicated to Hermann Maurer on the Occasion of His 70th Birthday","type":"book_chapter","publist_id":"2427","department":[{"_id":"HeEd"}],"status":"public","has_accepted_license":"1"}