[{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1707.02577","open_access":"1"}],"quality_controlled":"1","year":"2020","article_type":"original","date_published":"2020-11-01T00:00:00Z","issue":"11","date_created":"2022-07-27T13:58:58Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","volume":82,"oa":1,"month":"11","scopus_import":"1","oa_version":"Preprint","language":[{"iso":"eng"}],"title":"Dynamic clustering to minimize the sum of radii","publication":"Algorithmica","publisher":"Springer Nature","status":"public","intvolume":"        82","day":"01","arxiv":1,"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"}],"author":[{"full_name":"Henzinger, Monika H","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530"},{"last_name":"Leniowski","full_name":"Leniowski, Dariusz","first_name":"Dariusz"},{"first_name":"Claire","full_name":"Mathieu, Claire","last_name":"Mathieu"}],"type":"journal_article","doi":"10.1007/s00453-020-00721-7","publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"page":"3183-3194","article_processing_charge":"No","_id":"11674","citation":{"ista":"Henzinger M, Leniowski D, Mathieu C. 2020. Dynamic clustering to minimize the sum of radii. Algorithmica. 82(11), 3183–3194.","apa":"Henzinger, M., 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>","ama":"Henzinger M, 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>","ieee":"M. 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.","short":"M. Henzinger, D. Leniowski, C. Mathieu, Algorithmica 82 (2020) 3183–3194.","chicago":"Henzinger, Monika, 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, 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>."},"date_updated":"2024-11-04T11:41:57Z","extern":"1","external_id":{"arxiv":["1707.02577"]}}]