{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T00:10:02Z","timestamp":1748995802574,"version":"3.41.0"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319411675"},{"type":"electronic","value":"9783319411682"}],"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\/978-3-319-41168-2_3","type":"book-chapter","created":{"date-parts":[[2016,7,4]],"date-time":"2016-07-04T01:26:28Z","timestamp":1467595588000},"page":"26-38","source":"Crossref","is-referenced-by-count":1,"title":["On the Complexity of Clustering with Relaxed Size Constraints"],"prefix":"10.1007","author":[{"given":"Massimiliano","family":"Goldwurm","sequence":"first","affiliation":[]},{"given":"Jianyi","family":"Lin","sequence":"additional","affiliation":[]},{"given":"Francesco","family":"Sacc\u00e0","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,7,5]]},"reference":[{"key":"3_CR1","doi-asserted-by":"crossref","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, 245\u2013249 (2009)","journal-title":"Mach. Learn."},{"key":"3_CR2","doi-asserted-by":"crossref","DOI":"10.1201\/9781584889977","volume-title":"Constrained Clustering: Advances in Algorithms, Theory, and Applications","author":"S Basu","year":"2008","unstructured":"Basu, S., Davidson, I., Wagstaff, K.: Constrained Clustering: Advances in Algorithms, Theory, and Applications. Chapman and Hall\/CRC, Boca Raton (2008)"},{"issue":"1","key":"3_CR3","doi-asserted-by":"crossref","first-page":"125","DOI":"10.3233\/FI-2012-644","volume":"115","author":"A Bertoni","year":"2012","unstructured":"Bertoni, A., Goldwurm, M., Lin, J., Sacc\u00e0, F.: Size constrained distance clustering: separation properties and some complexity results. Fundamenta Informaticae 115(1), 125\u2013139 (2012)","journal-title":"Fundamenta Informaticae"},{"key":"3_CR4","doi-asserted-by":"crossref","unstructured":"Bertoni, A., R\u00e8, M., Sacc\u00e0, F., Valentini, G.: Identification of promoter regions in genomic sequences by 1-dimensional constraint clustering. In: Neural Nets WIRN11, pp. 162\u2013169 (2011)","DOI":"10.3233\/978-1-60750-972-1-162"},{"key":"3_CR5","volume-title":"Pattern Recognition and Machine Learning","author":"C Bishop","year":"2006","unstructured":"Bishop, C.: Pattern Recognition and Machine Learning. Springer, New York (2006)"},{"key":"3_CR6","unstructured":"Bradley, P.S., Bennett, K.P., Demiriz, A.: Constrained K-Means Clustering. Technical report MSR-TR-2000-65, Miscrosoft Research Publication, May 2000"},{"key":"3_CR7","unstructured":"Dasgupta, S.: The hardness of $$k$$ k -means clustering. Technical report CS2007-0890, Department of Computer Science and Engineering, University of California, San Diego (2007)"},{"issue":"284","key":"3_CR8","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1080\/01621459.1958.10501479","volume":"53","author":"WD Fisher","year":"1958","unstructured":"Fisher, W.D.: On grouping for maximum homogeneity. J. Am. Stat. Assoc. 53(284), 789\u2013798 (1958)","journal-title":"J. Am. Stat. Assoc."},{"key":"3_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/3-540-62495-3_45","volume-title":"Graph Drawing","author":"U F\u00f6\u00dfmeier","year":"1997","unstructured":"F\u00f6\u00dfmeier, U., Kant, G., Kaufmann, M.: 2-Visibility drawings of planar graphs. In: North, S. (ed.) Graph Drawing. LNCS, vol. 1190, pp. 155\u2013168. Springer, Heidelberg (1997)"},{"key":"3_CR10","unstructured":"Hasegawa, S., Imai, H., Inaba, M., Katoh, N.: Efficient algorithms for variance-based $$k$$ k -clustering. In: Proceedings of Pacific Graphics 1993, pp. 75\u201389 (1993)"},{"issue":"3","key":"3_CR11","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1137\/0405033","volume":"5","author":"DE Knuth","year":"1992","unstructured":"Knuth, D.E., Raghunathan, A.: The problem of compatible representatives. SIAM J. Discrete Math. 5(3), 422\u2013427 (1992)","journal-title":"SIAM J. Discrete Math."},{"issue":"2","key":"3_CR12","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1137\/0211025","volume":"11","author":"D Lichtenstein","year":"1982","unstructured":"Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput. 11(2), 329\u2013343 (1982)","journal-title":"SIAM J. Comput."},{"key":"3_CR13","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.tcs.2015.10.005","volume":"629","author":"J Lin","year":"2016","unstructured":"Lin, J., Bertoni, A., Goldwurm, M.: Exact algorithms for size constrained 2-clustering in the plane. Theor. Comput. Sci. 629, 80\u201395 (2016)","journal-title":"Theor. Comput. Sci."},{"issue":"2","key":"3_CR14","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/TIT.1982.1056489","volume":"28","author":"S Lloyd","year":"1982","unstructured":"Lloyd, S.: Least squares quantization in PCM. IEEE Trans. Inf. Theor. 28(2), 129\u2013137 (1982)","journal-title":"IEEE Trans. Inf. Theor."},{"key":"3_CR15","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, pp. 281\u2013297 (1967)"},{"key":"3_CR16","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.tcs.2010.05.034","volume":"442","author":"M Mahajan","year":"2012","unstructured":"Mahajan, 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."},{"issue":"2","key":"3_CR17","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1145\/1346330.1346336","volume":"55","author":"W Mulzer","year":"2008","unstructured":"Mulzer, W., Rote, G.: Minimum-weight triangulation is NP-hard. J. ACM 55(2), 11 (2008)","journal-title":"J. ACM"},{"key":"3_CR18","volume-title":"Combinatorial Optimization: Algorithms and Complexity","author":"C Papadimitriou","year":"1998","unstructured":"Papadimitriou, C., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover, New York (1998)"},{"issue":"335","key":"3_CR19","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1080\/01621459.1971.10482319","volume":"66","author":"MR Rao","year":"1971","unstructured":"Rao, M.R.: Cluster analysis and mathematical programming. J. Am. Stat. Assoc. 66(335), 622\u2013626 (1971)","journal-title":"J. Am. Stat. Assoc."},{"issue":"3","key":"3_CR20","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.disopt.2010.03.002","volume":"7","author":"R Stephan","year":"2010","unstructured":"Stephan, R.: Cardinality constrained combinatorial optimization: complexity and polyhedra. Discrete Optim. 7(3), 99\u2013113 (2010)","journal-title":"Discrete Optim."},{"key":"3_CR21","series-title":"Lecture Notes in Computer Science","first-page":"405","volume-title":"Database Theory - ICDT 2001","author":"AKH Tung","year":"2000","unstructured":"Tung, A.K.H., Han, J., Lakshmanan, L.V.S., Ng, R.T.: Constraint-based clustering in large databases. In: Van den Bussche, J., Vianu, V. (eds.) ICDT 2001. LNCS, vol. 1973, pp. 405\u2013419. Springer, Heidelberg (2000)"},{"issue":"4","key":"3_CR22","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1007\/s00454-011-9340-1","volume":"45","author":"A Vattani","year":"2011","unstructured":"Vattani, A.: $$k$$ k -means requires exponentially many iterations even in the plane. Discrete Comput. Geom. 45(4), 596\u2013616 (2011)","journal-title":"Discrete Comput. Geom."},{"key":"3_CR23","volume-title":"Approximation Algorithms","author":"V Vazirani","year":"2001","unstructured":"Vazirani, V.: Approximation Algorithms. Springer, Heidelberg (2001)"},{"issue":"326","key":"3_CR24","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1080\/01621459.1969.10500990","volume":"64","author":"H Vinod","year":"1969","unstructured":"Vinod, H.: Integer programming and the theory of grouping. J. Am. Stat. Assoc. 64(326), 506\u2013519 (1969)","journal-title":"J. Am. Stat. Assoc."},{"key":"3_CR25","unstructured":"Wagstaff, K., Cardie, C.: Clustering with instance-level constraints. In: Proceedings of the 17th International Conference on Machine Learning, pp. 1103\u20131110 (2000)"},{"issue":"8","key":"3_CR26","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1016\/j.knosys.2010.06.003","volume":"23","author":"S Zhu","year":"2010","unstructured":"Zhu, S., Wang, D., Li, T.: Data clustering with size constraints. Knowl. Based Syst. 23(8), 883\u2013889 (2010)","journal-title":"Knowl. Based Syst."}],"container-title":["Lecture Notes in Computer Science","Algorithmic Aspects in Information and Management"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-41168-2_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T23:43:46Z","timestamp":1748994226000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-41168-2_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319411675","9783319411682"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-41168-2_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]}}}