{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T10:54:27Z","timestamp":1756810467066},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T00:00:00Z","timestamp":1585612800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T00:00:00Z","timestamp":1585612800000},"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":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s00454-020-00190-3","type":"journal-article","created":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T23:23:07Z","timestamp":1585696987000},"page":"1199-1231","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Separation by Convex Pseudo-Circles"],"prefix":"10.1007","volume":"65","author":[{"given":"Nicolas","family":"Chevallier","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Augustin","family":"Fruchard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dominique","family":"Schmitt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Claude","family":"Spehner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,3,31]]},"reference":[{"key":"190_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-48447-7_1","volume-title":"Algorithms and Data Structures (Vancouver 1999)","author":"A Andrzejak","year":"1999","unstructured":"Andrzejak, A., Fukuda, K.: Optimization over $$k$$-set polytopes and efficient $$k$$-set enumeration. Algorithms and Data Structures (Vancouver 1999). Lecture Notes in Computer Science, vol. 1663, pp. 1\u201312. Springer, Berlin (1999)"},{"issue":"1","key":"190_CR2","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/s00454-002-2778-4","volume":"29","author":"A Andrzejak","year":"2003","unstructured":"Andrzejak, A., Welzl, E.: In between $$k$$-sets, $$j$$-facets, and $$i$$-faces: $$(i, j)$$-partitions. Discret. Comput. Geom. 29(1), 105\u2013131 (2003)","journal-title":"Discret. Comput. Geom."},{"key":"190_CR3","doi-asserted-by":"publisher","DOI":"10.1142\/8685","volume-title":"Voronoi Diagrams and Delaunay Triangulations","author":"F Aurenhammer","year":"2013","unstructured":"Aurenhammer, F., Klein, R., Lee, D.-T.: Voronoi Diagrams and Delaunay Triangulations. World Scientific, Hackensack (2013)"},{"issue":"4","key":"190_CR4","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1142\/S0218195992000214","volume":"2","author":"F Aurenhammer","year":"1992","unstructured":"Aurenhammer, F., Schwarzkopf, O.: A simple on-line randomized incremental algorithm for computing higher order Voronoi diagrams. Int. J. Comput. Geom. Appl. 2(4), 363\u2013381 (1992)","journal-title":"Int. J. Comput. Geom. Appl."},{"issue":"1","key":"190_CR5","first-page":"1","volume":"7","author":"M Axenovich","year":"2016","unstructured":"Axenovich, M., Ueckerdt, T.: Density of range capturing hypergraphs. J. Comput. Geom. 7(1), 1\u201321 (2016)","journal-title":"J. Comput. Geom."},{"key":"190_CR6","doi-asserted-by":"crossref","unstructured":"Buzaglo, S., Holzman, R., Pinchasi, R.: On $$s$$-intersecting curves and related problems. In: Proceedings of ACM Symposium on Computational Geometry (SCG\u201908), pp. 79\u201384. ACM, New York (2008)","DOI":"10.1145\/1377676.1377690"},{"key":"190_CR7","doi-asserted-by":"crossref","unstructured":"Buzaglo, S., Pinchasi, R., Rote G.: Topological hypergraphs. In: Thirty Essays on Geometric Graph Theory, pp. 71\u201381. Springer, New York (2013)","DOI":"10.1007\/978-1-4614-0110-0_6"},{"key":"190_CR8","doi-asserted-by":"crossref","unstructured":"Chevallier, N., Fruchard, A., Schmitt, D., Spehner, J.-C.: Separation by convex pseudo-circles. In: Proceedings of the 30th Annual Symposium on Computational Geometry (SoCG\u201914), pp. 444\u2013453, ACM, New York (2014)","DOI":"10.1145\/2582112.2582148"},{"key":"190_CR9","unstructured":"Chevallier, N., Fruchard, A., Schmitt, D., Spehner, J.-C.: Separation by convex pseudo-circles (2015). https:\/\/hal.archives-ouvertes.fr\/hal-01108235"},{"issue":"3","key":"190_CR10","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1007\/PL00009354","volume":"19","author":"TK Dey","year":"1998","unstructured":"Dey, T.K.: Improved bounds for planar $$k$$-sets and related problems. Discret. Comput. Geom. 19(3), 373\u2013382 (1998)","journal-title":"Discret. Comput. Geom."},{"issue":"4","key":"190_CR11","doi-asserted-by":"publisher","first-page":"865","DOI":"10.1007\/s00454-018-0049-2","volume":"62","author":"H Edelsbrunner","year":"2019","unstructured":"Edelsbrunner, H., Nikitenko, A.: Poisson\u2013Delaunay mosaics of order $$k$$. Discret. Comput. Geom. 62(4), 865\u2013878 (2019)","journal-title":"Discret. Comput. Geom."},{"issue":"3","key":"190_CR12","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/PL00009291","volume":"17","author":"H Edelsbrunner","year":"1997","unstructured":"Edelsbrunner, H., Valtr, P., Welzl, E.: Cutting dense point sets in half. Discret. Comput. Geom. 17(3), 243\u2013255 (1997)","journal-title":"Discret. Comput. Geom."},{"issue":"6","key":"190_CR13","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1142\/S0218195911003846","volume":"21","author":"W El Oraiby","year":"2011","unstructured":"El Oraiby, W., Schmitt, D., Spehner, J.-C.: Centroid triangulations from $$k$$-sets. Int. J. Comput. Geom. Appl. 21(6), 635\u2013659 (2011)","journal-title":"Int. J. Comput. Geom. Appl."},{"issue":"4","key":"190_CR14","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/0167-8396(86)90001-4","volume":"3","author":"CL Lawson","year":"1986","unstructured":"Lawson, C.L.: Properties of $$n$$-dimensional triangulations. Comput. Aided Geom. Des. 3(4), 231\u2013246 (1986)","journal-title":"Comput. Aided Geom. Des."},{"issue":"6","key":"190_CR15","first-page":"478","volume":"C\u201331","author":"D-T Lee","year":"1982","unstructured":"Lee, D.-T.: On $$k$$-nearest neighbor Voronoi diagrams in the plane. IEEE Trans. Comput. C\u201331(6), 478\u2013487 (1982)","journal-title":"IEEE Trans. Comput."},{"key":"190_CR16","doi-asserted-by":"crossref","unstructured":"Liu, Y., Snoeyink, J.: Quadratic and cubic B-splines by generalizing higher-order Voronoi diagrams. In: Proceedings of ACM Symposium on Computational Geometry (SCG\u201907), pp. 150\u2013157. ACM, New York (2007)","DOI":"10.1145\/1247069.1247100"},{"issue":"7","key":"190_CR17","doi-asserted-by":"publisher","first-page":"2993","DOI":"10.1090\/S0002-9947-07-03976-1","volume":"359","author":"M Neamtu","year":"2007","unstructured":"Neamtu, M.: Delaunay configurations and multivariate splines: A generalization of a result of B. N. Delaunay. Trans. Am. Math. Soc. 359(7), 2993\u20133004 (2007)","journal-title":"N. Delaunay. Trans. Am. Math. Soc."},{"key":"190_CR18","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/s11856-009-0076-z","volume":"172","author":"R Pinchasi","year":"2009","unstructured":"Pinchasi, R., Rote, G.: On the maximum size of an anti-chain of linearly separable sets and convex pseudo-discs. Israel J. Math. 172, 337\u2013348 (2009)","journal-title":"Israel J. Math."},{"issue":"1","key":"190_CR19","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/0097-3165(72)90019-2","volume":"13","author":"N Sauer","year":"1972","unstructured":"Sauer, N.: On the density of families of sets. J. Comb. Theory Ser. A 13(1), 145\u2013147 (1972)","journal-title":"J. Comb. Theory Ser. A"},{"key":"190_CR20","doi-asserted-by":"crossref","unstructured":"Schmitt, D.: Bivariate B-splines from convex pseudo-circle configurations. In: Fundamentals of Computation Theory. Lecture Notes in Computer Science, vol.\u00a011651, pp. 335\u2013349. Springer, Cham (2019)","DOI":"10.1007\/978-3-030-25027-0_23"},{"key":"190_CR21","unstructured":"Schmitt, D., Spehner, J.-C.: On Delaunay and Voronoi diagrams of order $$k$$ in the plane. In: Proceedings of the 3rd Canadian Conference on Computational Geometry (1991), pp. 29\u201332"},{"issue":"1","key":"190_CR22","doi-asserted-by":"publisher","first-page":"247","DOI":"10.2140\/pjm.1972.41.247","volume":"41","author":"S Shelah","year":"1972","unstructured":"Shelah, S.: A combinatorial problem; stability and order for models and theories in infinitary languages. Pac. J. Math. 41(1), 247\u2013261 (1972)","journal-title":"Pac. J. Math."},{"key":"190_CR23","first-page":"349","volume":"1","author":"J Steiner","year":"1826","unstructured":"Steiner, J.: Einige Gesetze \u00fcber die Theilung der Ebene und des Raumes. J. Reine Angew. Math. 1, 349\u2013364 (1826)","journal-title":"J. Reine Angew. Math."},{"issue":"2","key":"190_CR24","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s004540010022","volume":"26","author":"G T\u00f3th","year":"2001","unstructured":"T\u00f3th, G.: Point sets with many $$k$$-sets. Discret. Comput. Geom. 26(2), 187\u2013194 (2001)","journal-title":"Discret. Comput. Geom."},{"issue":"2","key":"190_CR25","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1137\/1116025","volume":"16","author":"VN Vapnik","year":"1971","unstructured":"Vapnik, V.N., Chervonenkis, A.Y.: On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16(2), 264\u2013280 (1971)","journal-title":"Theory Probab. Appl."}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00190-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-020-00190-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00190-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T15:36:46Z","timestamp":1619537806000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-020-00190-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,31]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["190"],"URL":"https:\/\/doi.org\/10.1007\/s00454-020-00190-3","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,31]]},"assertion":[{"value":"26 December 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 January 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 February 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 March 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}