{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T05:21:56Z","timestamp":1772515316706,"version":"3.50.1"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p> Let P be a d-dimensional n-point set. A partition [Formula: see text] of P is called a Tverberg partition if the convex hulls of all sets in [Formula: see text] intersect in at least one point. We say that [Formula: see text] is t-tolerant if it remains a Tverberg partition after deleting any t points from P. Sober\u00f3n and Strausz proved that there is always a t-tolerant Tverberg partition with \u2308n\/(d + 1)(t + 1)\u2309 sets. However, no nontrivial algorithms for computing or approximating such partitions have been presented so far. <\/jats:p><jats:p> For d \u2264 2, we show that the Sober\u00f3n-Strausz bound can be improved, and we show how the corresponding partitions can be found in polynomial time. For d \u2265 3, we give the first polynomial-time approximation algorithm by presenting a reduction to the regular Tverberg problem (with no tolerance). Finally, we show that it is coNP-complete to determine whether a given Tverberg partition is t-tolerant. <\/jats:p>","DOI":"10.1142\/s0218195914600073","type":"journal-article","created":{"date-parts":[[2015,5,25]],"date-time":"2015-05-25T11:11:58Z","timestamp":1432552318000},"page":"261-273","source":"Crossref","is-referenced-by-count":9,"title":["ALGORITHMS FOR TOLERANT TVERBERG PARTITIONS"],"prefix":"10.1142","volume":"24","author":[{"given":"WOLFGANG","family":"MULZER","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, Takustr. 9, 14195 Berlin, Germany"}]},{"given":"YANNIK","family":"STEIN","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, Takustr. 9, 14195 Berlin, Germany"}]}],"member":"219","published-online":{"date-parts":[[2015,5,25]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1142\/S021819599600023X"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/4.1.6"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2010.04.006"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-010-9296-6"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-013-9528-7"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-21.4.291"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.2000.0492"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02808223"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-011-9379-z"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-41.1.123"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195914600073","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:40:54Z","timestamp":1565185254000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195914600073"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12]]},"references-count":10,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2015,5,25]]},"published-print":{"date-parts":[[2014,12]]}},"alternative-id":["10.1142\/S0218195914600073"],"URL":"https:\/\/doi.org\/10.1142\/s0218195914600073","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12]]}}}