{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:39:20Z","timestamp":1773250760376,"version":"3.50.1"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319334608","type":"print"},{"value":"9783319334615","type":"electronic"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-33461-5_2","type":"book-chapter","created":{"date-parts":[[2016,5,24]],"date-time":"2016-05-24T22:35:59Z","timestamp":1464129359000},"page":"14-25","source":"Crossref","is-referenced-by-count":3,"title":["Centerpoints: A Link Between Optimization and Convex Geometry"],"prefix":"10.1007","author":[{"given":"Amitabh","family":"Basu","sequence":"first","affiliation":[]},{"given":"Timm","family":"Oertel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,5,25]]},"reference":[{"issue":"3","key":"2_CR1","doi-asserted-by":"crossref","first-page":"1610","DOI":"10.1137\/110850463","volume":"27","author":"G Averkov","year":"2013","unstructured":"Averkov, G.: On maximal S-free sets and the helly number for the family of s-convex sets. SIAM J. Discrete Math. 27(3), 1610\u20131624 (2013)","journal-title":"SIAM J. Discrete Math."},{"issue":"1","key":"2_CR2","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1515\/advgeom.2011.028","volume":"12","author":"G Averkov","year":"2012","unstructured":"Averkov, G., Weismantel, R.: Transversal numbers over subsets of linear spaces. Adv. Geom. 12(1), 19\u201328 (2012)","journal-title":"Adv. Geom."},{"issue":"01","key":"2_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1112\/S0025579312000101","volume":"59","author":"V Baldoni","year":"2013","unstructured":"Baldoni, V., Berline, N., Koeppe, M., Vergne, M.: Intermediate sums on polyhedra: computation and real Ehrhart theory. Mathematika 59(01), 1\u201322 (2013)","journal-title":"Mathematika"},{"issue":"4","key":"2_CR4","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1145\/1008731.1008733","volume":"51","author":"D Bertsimas","year":"2004","unstructured":"Bertsimas, D., Vempala, S.: Solving convex programs by random walks. J. ACM 51(4), 540\u2013556 (2004)","journal-title":"J. ACM"},{"issue":"05","key":"2_CR5","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1142\/S021819590300127X","volume":"13","author":"P Bra\u00df","year":"2003","unstructured":"Bra\u00df, P., Heinrich-Litan, L., Morin, P.: Computing the center of area of a convex polygon. Int. J. Comput. Geom. Appl. 13(05), 439\u2013445 (2003)","journal-title":"Int. J. Comput. Geom. Appl."},{"key":"2_CR6","unstructured":"De Loera, J.A., La Haye, R.N., Oliveros, D., Rold\u00e1n-Pensado, E.: Helly numbers of algebraic subsets of $$\\mathbb{R}^d$$ . arXiv preprint arXiv:1508.02380 (2015)"},{"key":"2_CR7","doi-asserted-by":"crossref","unstructured":"Dyckerhoff, R., Mozharovskyi, P.: Exact computation of halfspace depth. arXiv preprint arXiv:1411.6927v2 (2015)","DOI":"10.1016\/j.csda.2015.12.011"},{"key":"2_CR8","series-title":"Algorithms and Combinatorics: Study and Research Texts","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-97881-4","volume-title":"Geometric Algorithms and Combinatorial Optimization","author":"M Gr\u00f6tschel","year":"1988","unstructured":"Gr\u00f6tschel, M., Lov\u00e1sz, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Algorithms and Combinatorics: Study and Research Texts, vol. 2. Springer, Berlin (1988)"},{"key":"2_CR9","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.2140\/pjm.1960.10.1257","volume":"10","author":"B Gr\u00fcnbaum","year":"1960","unstructured":"Gr\u00fcnbaum, B.: Partitions of mass-distributions and of convex bodies by hyperplanes. Pac. J. Math. 10, 1257\u20131261 (1960)","journal-title":"Pac. J. Math."},{"key":"2_CR10","doi-asserted-by":"crossref","unstructured":"Gr\u00fcnbaum, B.: Measures of symmetry for convex sets. In: Convexity: Proceedings of the Seventh Symposium in Pure Mathematics of the American Mathematical Society, vol. 7, p. 233. American Mathematical Society (1963)","DOI":"10.1090\/pspum\/007\/0156259"},{"key":"2_CR11","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1111\/j.1749-6632.1979.tb32803.x","volume":"319","author":"AJ Hoffman","year":"1979","unstructured":"Hoffman, A.J.: Binding constraints and helly numbers. Ann. N. Y. Acad. Sci. 319, 284\u2013288 (1979)","journal-title":"Ann. N. Y. Acad. Sci."},{"issue":"3","key":"2_CR12","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1007\/BF01442795","volume":"6","author":"AN Korkine","year":"1873","unstructured":"Korkine, A.N., Zolotareff, Y.I.: Sur les formes quadratiques. Math. Ann. 6(3), 366\u2013389 (1873)","journal-title":"Math. Ann."},{"issue":"4","key":"2_CR13","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1287\/moor.8.4.538","volume":"8","author":"HW Lenstra Jr","year":"1983","unstructured":"Lenstra Jr., H.W.: Integer programming with a fixed number of variables. Math. Oper. Res. 8(4), 538\u2013548 (1983)","journal-title":"Math. Oper. Res."},{"key":"2_CR14","doi-asserted-by":"crossref","DOI":"10.1090\/dimacs\/072","volume-title":"Data Depth: Robust Multivariate Analysis, Computational Geometry, and Applications","author":"RY Liu","year":"2006","unstructured":"Liu, R.Y., Serfling, R.J., Souvaine, D.L.: Data Depth: Robust Multivariate Analysis, Computational Geometry, and Applications, vol. 72. American Mathematical Society, Providence (2006)"},{"key":"2_CR15","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/978-3-642-35494-6_2","volume-title":"Robustness and Complex Data Structures","author":"K Mosler","year":"2013","unstructured":"Mosler, K.: Depth statistics. In: Becker, C., Fried, R., Kuhnt, S. (eds.) Robustness and Complex Data Structures, pp. 17\u201334. Springer, Heidelberg (2013)"},{"key":"2_CR16","series-title":"Applied Optimization","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory Lectures on Convex Optimization","author":"Y Nesterov","year":"2004","unstructured":"Nesterov, Y.: Introductory Lectures on Convex Optimization. Applied Optimization, vol. 87. Kluwer Academic Publishers, Boston (2004)"},{"key":"2_CR17","doi-asserted-by":"crossref","unstructured":"Pak, I.: On sampling integer points in polyhedra. In: Foundations of computational mathematics (Hong Kong, 2000), pp. 319\u2013324. World Sci. Publ., River Edge (2002)","DOI":"10.1142\/9789812778031_0013"},{"issue":"3","key":"2_CR18","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/PL00020903","volume":"49","author":"PJ Rousseeuw","year":"1999","unstructured":"Rousseeuw, P.J., Ruts, I.: The depth function of a population distribution. Metrika 49(3), 213\u2013244 (1999)","journal-title":"Metrika"},{"key":"2_CR19","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1214\/aop\/1176988847","volume":"22","author":"M Talagrand","year":"1994","unstructured":"Talagrand, M.: Sharper bounds for gaussian and empirical processes. Ann. Probab. 22, 28\u201376 (1994)","journal-title":"Ann. Probab."},{"key":"2_CR20","unstructured":"Tukey, J.W.: Mathematics and the picturing of data. In: Proceedings of the International Congress of Mathematicians, vol. 2, pp. 523\u2013531 (1975)"},{"key":"2_CR21","doi-asserted-by":"crossref","unstructured":"Vapnik, V.N., Chervonenkis, A.Ya.: On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16(2), 264\u2013280 (1971)","DOI":"10.1137\/1116025"}],"container-title":["Lecture Notes in Computer Science","Integer Programming and Combinatorial Optimization"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-33461-5_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,18]],"date-time":"2023-08-18T16:06:19Z","timestamp":1692374779000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-33461-5_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319334608","9783319334615"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-33461-5_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]}}}