{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T01:57:12Z","timestamp":1778205432873,"version":"3.51.4"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T00:00:00Z","timestamp":1645142400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T00:00:00Z","timestamp":1645142400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2022,8]]},"DOI":"10.1007\/s00493-020-4633-8","type":"journal-article","created":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T11:24:41Z","timestamp":1645183481000},"page":"463-490","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Computing the Covering Radius of a Polytope with an Application to Lonely Runners"],"prefix":"10.1007","volume":"42","author":[{"given":"Jana","family":"Cslovjecsek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Romanos Diogenes","family":"Malikiosis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M\u00e1rton","family":"Nasz\u00f3di","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthias","family":"Schymura","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,2,18]]},"reference":[{"key":"4633_CR1","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/s10107-015-0865-6","volume":"154","author":"G Averkov","year":"2015","unstructured":"G. Averkov and A. Basu: Lifting properties of maximal lattice-free polyhedra, Math. Program. 154 (2015), 81\u2013111.","journal-title":"Math. Program."},{"key":"4633_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s13366-011-0028-8","volume":"53","author":"G Averkov","year":"2012","unstructured":"G. Averkov and C. Wagner: Inequalities for the lattice width of lattice-free convex sets in the plane, Beitr. Algebra Geom. 53 (2012), 1\u201323.","journal-title":"Beitr. Algebra Geom."},{"key":"4633_CR3","doi-asserted-by":"publisher","first-page":"5687","DOI":"10.1016\/j.disc.2008.04.041","volume":"309","author":"J Barajas","year":"2009","unstructured":"J. Barajas and O. Serra: On the chromatic number of circulant graphs, Discrete Math. 309 (2009), 5687\u20135696.","journal-title":"Discrete Math."},{"key":"4633_CR4","series-title":"Graduate Studies in Mathematics","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/054","volume-title":"A course in convexity","author":"A Barvinok","year":"2002","unstructured":"A. Barvinok: A course in convexity, Graduate Studies in Mathematics, vol. 54, American Mathematical Society, Providence, RI, 2002."},{"key":"4633_CR5","first-page":"#A29","volume":"19","author":"M Beck","year":"2019","unstructured":"M. Beck, S. Ho\u015ften and M. Schymura: Lonely Runner Polyhedra, Integers 19 (2019), #A29.","journal-title":"Integers"},{"key":"4633_CR6","doi-asserted-by":"crossref","unstructured":"T. Bohman, R. Holzman and D. Kleitman: Six lonely runners, Electron. J. Combin. 8 (2001), Research Paper 3, (electronic). In honor of Aviezri Fraenkel on the occasion of his 70th birthday.","DOI":"10.37236\/1602"},{"key":"4633_CR7","doi-asserted-by":"publisher","first-page":"4814","DOI":"10.1016\/j.tcs.2011.02.009","volume":"412","author":"\u00c9 Charrier","year":"2011","unstructured":"\u00c9. Charrier, F. Feschet and L. Buzer: Computing efficiently the lattice width in any dimension, Theoret. Comput. Sci. 412 (2011), 4814\u20134823.","journal-title":"Theoret. Comput. Sci."},{"key":"4633_CR8","doi-asserted-by":"crossref","unstructured":"G. Codenotti, F. Santos and M. Schymura: The covering radius and a discrete surface area for non-hollow simplices, Discrete Comput. Geom. (2021), to appear, https:\/\/arxiv.org\/abs\/1903.02866.","DOI":"10.1007\/s00454-021-00330-3"},{"key":"4633_CR9","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/BF01832623","volume":"9","author":"T W Cusick","year":"1973","unstructured":"Th. W. Cusick: View-obstruction problems, Aequat. Math. 9 (1973), 165\u2013170.","journal-title":"Aequat. Math."},{"key":"4633_CR10","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.ipl.2008.03.019","volume":"108","author":"S Czerwi\u0144ski","year":"2008","unstructured":"S. Czerwi\u0144ski and J. Grytczuk: Invisible runners in finite fields, Inf. Process. Lett. 108 (2008), 64\u201367.","journal-title":"Inf. Process. Lett."},{"key":"4633_CR11","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/s10107-013-0654-z","volume":"145","author":"S Dash","year":"2014","unstructured":"S. Dash, N. B. Dobbs, O. G\u00fcnl\u00fck, T. J. Nowicki and G. M. \u015awirszcz: Latticefree sets, multi-branch split disjunctions, and mixed-integer programming, Math. Program. 145 (2014), 483\u2013508.","journal-title":"Math. Program."},{"key":"4633_CR12","series-title":"North-Holland Mathematical Library","volume-title":"Geometry of Numbers","author":"P M Gruber","year":"1987","unstructured":"P. M. Gruber and C. G. Lekkerkerker: Geometry of Numbers, second ed., North-Holland Mathematical Library, vol. 37, North-Holland Publishing Co., Amsterdam, 1987.","edition":"second ed."},{"key":"4633_CR13","unstructured":"I. Haviv and O. Regev: Hardness of the covering radius problem on lattices, Chic. J. Theoret. Comput. Sci. (2012), Article 4."},{"key":"4633_CR14","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s00010-016-0458-3","volume":"91","author":"M Henze","year":"2017","unstructured":"M. Henze and R.-D. Malikiosis: On the covering radius of lattice zonotopes and its relation to view-obstructions and the lonely runner conjecture, Aequat. Math. 91 (2017), 331\u2013352.","journal-title":"Aequat. Math."},{"key":"4633_CR15","doi-asserted-by":"publisher","first-page":"6605","DOI":"10.1090\/tran\/7531","volume":"371","author":"O Iglesias-Vali\u00f1o","year":"2019","unstructured":"O. Iglesias-Vali\u00f1o and F. Santos: Classification of empty lattice 4-simplices of width larger than two, Trans. Amer. Math. Soc. 371 (2019), 6605\u20136625.","journal-title":"Trans. Amer. Math. Soc."},{"key":"4633_CR16","series-title":"Polyhedral Combinatorics, DIMACS Series in Discrete Mathematics and Theoretical Computer Science","first-page":"39","volume-title":"Test sets for integer programs, \u2200\u2203 sentences","author":"R Kannan","year":"1990","unstructured":"R. Kannan: Test sets for integer programs, \u2200\u2203 sentences, Polyhedral Combinatorics, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 1, Providence, RI, American Mathematical Society, 1990, 39\u201347."},{"key":"4633_CR17","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/BF01204720","volume":"12","author":"R Kannan","year":"1992","unstructured":"R. Kannan: Lattice translates of a polytope and the Frobenius problem, Combinatorica 12 (1992), 161\u2013177.","journal-title":"Combinatorica"},{"key":"4633_CR18","doi-asserted-by":"publisher","first-page":"577","DOI":"10.2307\/1971436","volume":"128","author":"R Kannan","year":"1988","unstructured":"R. Kannan and L. Lov\u00e1sz: Covering minima and lattice-point-free convex bodies, Ann. of Math. (2) 128 (1988), 577\u2013602.","journal-title":"Ann. of Math. (2)"},{"key":"4633_CR19","unstructured":"N. Kravitz: Barely lonely runners and very lonely runners, https:\/\/arxiv.org\/abs\/1912.06034, 2019."},{"key":"4633_CR20","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1287\/moor.8.4.538","volume":"8","author":"H W Lenstra","year":"1983","unstructured":"H. W. Lenstra: Integer programming with a fixed number of variables, Math. Oper. Res. 8 (1983), 538\u2013548.","journal-title":"Math. Oper. Res."},{"key":"4633_CR21","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/0607052","volume":"7","author":"O L Mangasarian","year":"1986","unstructured":"O. L. Mangasarian and T.-H. Shiau: A Variable-Complexity Norm Maximization Problem, SIAM J. Alg. Disc. Meth. 7 (1986), 455\u2013461.","journal-title":"SIAM J. Alg. Disc. Meth."},{"key":"4633_CR22","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1137\/S0097539703433511","volume":"34","author":"D Micciancio","year":"2004","unstructured":"D. Micciancio: Almost perfect lattices, the covering radius problem, and applications to Ajtai\u2019s connection factor, SIAM J. Comput. 34 (2004), 118\u2013169.","journal-title":"SIAM J. Comput."},{"key":"4633_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0897-7","volume-title":"Complexity of lattice problems. A cryptographic perspective","author":"D Micciancio","year":"2002","unstructured":"D. Micciancio and S. Goldwasser: Complexity of lattice problems. A cryptographic perspective, vol. 671, Boston, MA: Kluwer Academic Publishers, 2002."},{"key":"4633_CR24","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/s10107-018-1323-z","volume":"179","author":"J Paat","year":"2020","unstructured":"J. Paat, R. Weismantel and S. Weltge: Distances between optimal solutions of mixed-integer programs, Math. Program. 179 (2020), 455\u2013468.","journal-title":"Math. Program."},{"key":"4633_CR25","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1023\/A:1009842406728","volume":"4","author":"M Rudelson","year":"2000","unstructured":"M. Rudelson: Distances between non-symmetric convex bodies and the MM*-estimate, Positivity 4 (2000), 161\u2013178.","journal-title":"Positivity"},{"key":"4633_CR26","doi-asserted-by":"crossref","unstructured":"I. J. Schoenberg: Extremum problems for the motions of a billiard ball, II. The L\u221e norm, in: Indag. Math., Nederl. Akad. Wetensch. Proc. Ser. A. 38, 263\u2013279, 1976.","DOI":"10.1016\/1385-7258(76)90053-6"},{"key":"4633_CR27","first-page":"14","volume":"26","author":"M Schymura","year":"2018","unstructured":"M. Schymura and J. M. Wills: Der einsame L\u00e4ufer, Mitt. Dtsch. Math.-Ver. 26 (2018), 14\u201317.","journal-title":"Mitt. Dtsch. Math.-Ver."},{"key":"4633_CR28","first-page":"1","volume":"13","author":"T Tao","year":"2018","unstructured":"T. Tao: Some remarks on the lonely runner conjecture, Contrib. Discrete Math. 13 (2018), 1\u201331.","journal-title":"Contrib. Discrete Math."},{"key":"4633_CR29","unstructured":"The Sage Developers: Sagemath, the Sage Mathematics Software System (Version 9.1), 2020, https:\/\/www.sagemath.org."},{"key":"4633_CR30","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1007\/BF01362551","volume":"72","author":"J M Wills","year":"1968","unstructured":"J. M. Wills: Zur simultanen homogenen diophantischen Approximation. I, Monatsh. Math. 72 (1968), 254\u2013263.","journal-title":"Monatsh. Math."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-020-4633-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00493-020-4633-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-020-4633-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,3]],"date-time":"2022-10-03T15:04:28Z","timestamp":1664809468000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00493-020-4633-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,18]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["4633"],"URL":"https:\/\/doi.org\/10.1007\/s00493-020-4633-8","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,18]]},"assertion":[{"value":"5 October 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 May 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 February 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}