{"page":"3183-3194","oa_version":"Preprint","volume":82,"title":"Dynamic clustering to minimize the sum of radii","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"11","issue":"11","extern":"1","type":"journal_article","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1707.02577","open_access":"1"}],"date_published":"2020-11-01T00:00:00Z","language":[{"iso":"eng"}],"date_updated":"2022-09-12T08:50:14Z","abstract":[{"text":"In this paper, we study the problem of opening centers to cluster a set of clients in a metric space so as to minimize the sum of the costs of the centers and of the cluster radii, in a dynamic environment where clients arrive and depart, and the solution must be updated efficiently while remaining competitive with respect to the current optimal solution. We call this dynamic sum-of-radii clustering problem. We present a data structure that maintains a solution whose cost is within a constant factor of the cost of an optimal solution in metric spaces with bounded doubling dimension and whose worst-case update time is logarithmic in the parameters of the problem.","lang":"eng"}],"_id":"11674","doi":"10.1007/s00453-020-00721-7","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","full_name":"Henzinger, Monika H","first_name":"Monika H","last_name":"Henzinger","orcid":"0000-0002-5008-6530"},{"first_name":"Dariusz","full_name":"Leniowski, Dariusz","last_name":"Leniowski"},{"last_name":"Mathieu","first_name":"Claire","full_name":"Mathieu, Claire"}],"publisher":"Springer Nature","scopus_import":"1","intvolume":"        82","citation":{"apa":"Henzinger, M. H., Leniowski, D., &#38; Mathieu, C. (2020). Dynamic clustering to minimize the sum of radii. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00453-020-00721-7\">https://doi.org/10.1007/s00453-020-00721-7</a>","short":"M.H. Henzinger, D. Leniowski, C. Mathieu, Algorithmica 82 (2020) 3183–3194.","ama":"Henzinger MH, Leniowski D, Mathieu C. Dynamic clustering to minimize the sum of radii. <i>Algorithmica</i>. 2020;82(11):3183-3194. doi:<a href=\"https://doi.org/10.1007/s00453-020-00721-7\">10.1007/s00453-020-00721-7</a>","chicago":"Henzinger, Monika H, Dariusz Leniowski, and Claire Mathieu. “Dynamic Clustering to Minimize the Sum of Radii.” <i>Algorithmica</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00453-020-00721-7\">https://doi.org/10.1007/s00453-020-00721-7</a>.","mla":"Henzinger, Monika H., et al. “Dynamic Clustering to Minimize the Sum of Radii.” <i>Algorithmica</i>, vol. 82, no. 11, Springer Nature, 2020, pp. 3183–94, doi:<a href=\"https://doi.org/10.1007/s00453-020-00721-7\">10.1007/s00453-020-00721-7</a>.","ista":"Henzinger MH, Leniowski D, Mathieu C. 2020. Dynamic clustering to minimize the sum of radii. Algorithmica. 82(11), 3183–3194.","ieee":"M. H. Henzinger, D. Leniowski, and C. Mathieu, “Dynamic clustering to minimize the sum of radii,” <i>Algorithmica</i>, vol. 82, no. 11. Springer Nature, pp. 3183–3194, 2020."},"status":"public","date_created":"2022-07-27T13:58:58Z","external_id":{"arxiv":["1707.02577"]},"publication":"Algorithmica","article_type":"original","oa":1,"quality_controlled":"1","year":"2020","publication_status":"published","day":"01"}