{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T01:00:43Z","timestamp":1740099643186,"version":"3.37.3"},"publisher-location":"Cham","reference-count":13,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030406158"},{"type":"electronic","value":"9783030406165"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-40616-5_35","type":"book-chapter","created":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T06:02:59Z","timestamp":1581573779000},"page":"394-399","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exact Linear-Time Algorithm for Parameterized K-Means Problem with Optimized Number of Clusters in the 1D Case"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7757-7228","authenticated-orcid":false,"given":"Alexander","family":"Kel\u2019manov","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2978-8340","authenticated-orcid":false,"given":"Vladimir","family":"Khandeev","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,2,14]]},"reference":[{"key":"35_CR1","unstructured":"Fisher, R.A.: Statistical Methods and Scientific Inference. Hafner, New York (1956)"},{"key":"35_CR2","unstructured":"MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281\u2013297. University of California Press, Berkeley (1967)"},{"key":"35_CR3","doi-asserted-by":"crossref","unstructured":"Inaba, M., Katoh, N., Imai, H.: Applications of weighted Voronoidiagrams and randomization to variance-based clustering. In: Proceedings of Annual Symposium on Computational Geometry, pp. 332\u2013339 (1994)","DOI":"10.1145\/177424.178042"},{"issue":"2","key":"35_CR4","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/s10994-009-5103-0","volume":"75","author":"D Aloise","year":"2009","unstructured":"Aloise, D., Deshpande, A., Hansen, P., Popat, P.: NP-hardness of Euclidean sum-of-squares clustering. Mach. Learn. 75(2), 245\u2013248 (2009)","journal-title":"Mach. Learn."},{"key":"35_CR5","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.tcs.2010.05.034","volume":"442","author":"M Mahajana","year":"2012","unstructured":"Mahajana, M., Nimbhorkar, P., Varadarajan, K.: The planar $$k$$-means problem is NP-hard. Theor. Comput. Sci. 442, 13\u201321 (2012)","journal-title":"Theor. Comput. Sci."},{"key":"35_CR6","doi-asserted-by":"publisher","first-page":"622","DOI":"10.1080\/01621459.1971.10482319","volume":"66","author":"M Rao","year":"1971","unstructured":"Rao, M.: Cluster analysis and mathematical programming. J. Am. Stat. Assoc. 66, 622\u2013626 (1971)","journal-title":"J. Am. Stat. Assoc."},{"key":"35_CR7","volume-title":"Dynamic Programming","author":"R Bellman","year":"1957","unstructured":"Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957)"},{"key":"35_CR8","unstructured":"Gr\u00f8nlund, A., Larsen, K.G., Mathiasen, A., Nielsen, J.S., Schneider, S., Song, M.: Fast exact $$k$$-means, $$k$$-medians and Bregman divergence clustering in 1D. CoRR \narXiv:1701.07204\n\n (2017)"},{"issue":"4","key":"35_CR9","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1016\/0196-6774(91)90039-2","volume":"12","author":"W Xiaolin","year":"1991","unstructured":"Xiaolin, W.: Optimal quantization by matrix searching. J. Algorithms 12(4), 663\u2013673 (1991)","journal-title":"J. Algorithms"},{"key":"35_CR10","first-page":"10","volume":"4","author":"NI Glebov","year":"1965","unstructured":"Glebov, N.I.: On the convex sequences. Discrete Anal. 4, 10\u201322 (1965). (In Russian)","journal-title":"Discrete Anal."},{"key":"35_CR11","first-page":"77","volume":"2","author":"EK Gimadutdinov","year":"1969","unstructured":"Gimadutdinov, E.K.: On the properties of solutions of one location problem of points on a segment. Control. Syst. 2, 77\u201391 (1969). (In Russian)","journal-title":"Control. Syst."},{"key":"35_CR12","first-page":"101","volume":"3","author":"EK Gimadutdinov","year":"1969","unstructured":"Gimadutdinov, E.K.: On one class of nonlinear programming problems. Control. Syst. 3, 101\u2013113 (1969). (In Russian)","journal-title":"Control. Syst."},{"key":"35_CR13","first-page":"3","volume":"27","author":"EK Gimadutdinov","year":"1987","unstructured":"Gimadutdinov, E.K.: Some standartization problems with arbitrary sign instances and coherent, quasi-convex and almost quasi-convex matrices. Control. Syst. 27, 3\u201311 (1987). (In Russian)","journal-title":"Control. Syst."}],"container-title":["Lecture Notes in Computer Science","Numerical Computations: Theory and Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-40616-5_35","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T06:08:13Z","timestamp":1581574093000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-40616-5_35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030406158","9783030406165"],"references-count":13,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-40616-5_35","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"14 February 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"NUMTA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Numerical Computations: Theory and Algorithms","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Crotone","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 June 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 June 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"numta2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/si.deis.unical.it\/~yaro\/numta2019\/index.php","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}