{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:26:27Z","timestamp":1777645587218,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T00:00:00Z","timestamp":1644883200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2022,2,15]]},"abstract":"<jats:p>\n                    The k-center problem is to choose a subset of size k from a set of n points such that the maximum distance from each point to its nearest center is minimized. Let Q = { Q\n                    <jats:sub>1<\/jats:sub>\n                    , . . . , Q\n                    <jats:sub>n<\/jats:sub>\n                    } be a set of polygons or segments in the region-based uncertainty model, in which each Q\n                    <jats:sub>i<\/jats:sub>\n                    is an uncertain point, where the exact locations of the points in Q\n                    <jats:sub>i<\/jats:sub>\n                    are unknown. The geometric objects such as segments and polygons can be models of a point set. We define the uncertain version of the k-center problem as a generalization in which the objective is to find k points from Q to cover the remaining regions of Q with minimum or maximum radius of the cluster to cover at least one or all exact instances of each Q\n                    <jats:sub>i<\/jats:sub>\n                    , respectively. We modify the region-based model to allow multiple points to be chosen from a region, and call the resulting model the aggregated uncertainty model.\n                  <\/jats:p>\n                  <jats:p>All these problems contain the point version as a special case, so they are all NP-hard with a lower bound 1.822 for the approximation factor. We give approximation algorithms for uncertain k-center of a set of segments and polygons. We also have implemented some of our algorithms on a data-set to show our theoretical performance guarantees can be achieved in practice.<\/jats:p>","DOI":"10.3233\/fi-2021-2097","type":"journal-article","created":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T12:34:10Z","timestamp":1644928450000},"page":"205-231","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Clustering Geometrically-Modeled Points in the Aggregated Uncertainty Model"],"prefix":"10.1177","volume":"184","author":[{"given":"Vahideh","family":"Keikha","sequence":"first","affiliation":[{"name":"The Czech Academy of Sciences, Institute of Computer Science, Prague, Czech Republic."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sepideh","family":"Aghamolaei","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Sharif University of Technology, Tehran, Iran."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"Mohades","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sci., Amirkabir University of Technology, Tehran, Iran."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad","family":"Ghodsi","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Sharif University of Technology, Tehran, Iran."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2022,2,15]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2021-2097","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2021-2097","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:32:39Z","timestamp":1777444359000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2021-2097"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,15]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,2,15]]}},"alternative-id":["10.3233\/FI-2021-2097"],"URL":"https:\/\/doi.org\/10.3233\/fi-2021-2097","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,15]]}}}