{"title":"On center regions and balls containing many points","date_updated":"2021-01-12T06:57:27Z","date_created":"2018-12-11T11:57:38Z","author":[{"first_name":"Shakhar","last_name":"Smorodinsky","full_name":"Smorodinsky, Shakhar"},{"last_name":"Sulovský","first_name":"Marek","full_name":"Sulovský, Marek"},{"orcid":"0000-0002-1494-0568","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","full_name":"Uli Wagner"}],"intvolume":"      5092","alternative_title":["LNCS"],"doi":"10.1007/978-3-540-69733-6_36","quality_controlled":0,"_id":"2432","year":"2008","day":"01","page":"363 - 373","citation":{"ieee":"S. Smorodinsky, M. Sulovský, and U. Wagner, “On center regions and balls containing many points,” presented at the COCOON: Conference on Computing and Combinatorics, 2008, vol. 5092, pp. 363–373.","short":"S. Smorodinsky, M. Sulovský, U. Wagner, in:, Springer, 2008, pp. 363–373.","apa":"Smorodinsky, S., Sulovský, M., &#38; Wagner, U. (2008). On center regions and balls containing many points (Vol. 5092, pp. 363–373). Presented at the COCOON: Conference on Computing and Combinatorics, Springer. <a href=\"https://doi.org/10.1007/978-3-540-69733-6_36\">https://doi.org/10.1007/978-3-540-69733-6_36</a>","chicago":"Smorodinsky, Shakhar, Marek Sulovský, and Uli Wagner. “On Center Regions and Balls Containing Many Points,” 5092:363–73. Springer, 2008. <a href=\"https://doi.org/10.1007/978-3-540-69733-6_36\">https://doi.org/10.1007/978-3-540-69733-6_36</a>.","ama":"Smorodinsky S, Sulovský M, Wagner U. On center regions and balls containing many points. In: Vol 5092. Springer; 2008:363-373. doi:<a href=\"https://doi.org/10.1007/978-3-540-69733-6_36\">10.1007/978-3-540-69733-6_36</a>","mla":"Smorodinsky, Shakhar, et al. <i>On Center Regions and Balls Containing Many Points</i>. Vol. 5092, Springer, 2008, pp. 363–73, doi:<a href=\"https://doi.org/10.1007/978-3-540-69733-6_36\">10.1007/978-3-540-69733-6_36</a>.","ista":"Smorodinsky S, Sulovský M, Wagner U. 2008. On center regions and balls containing many points. COCOON: Conference on Computing and Combinatorics, LNCS, vol. 5092, 363–373."},"publisher":"Springer","month":"01","extern":1,"volume":5092,"publication_status":"published","publist_id":"4482","type":"conference","date_published":"2008-01-01T00:00:00Z","conference":{"name":"COCOON: Conference on Computing and Combinatorics"},"abstract":[{"lang":"eng","text":"We study the disk containment problem introduced by Neumann-Lara and Urrutia and its generalization to higher dimensions. We relate the problem to centerpoints and lower centerpoints of point sets. Moreover, we show that for any set of n points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing A contains at least roughly 4/5ed 3n points of S. This improves previous bounds for which the constant was exponentially small in d. We also consider a generalization of the planar disk containment problem to families of pseudodisks."}],"status":"public"}