{"links":{},"metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00106920","sets":["1164:2592:7425:7738"]},"path":["7738"],"owner":"11","recid":"106920","title":["Approximating the Colorful Caratheodory Theorem"],"pubdate":{"attribute_name":"公開日","attribute_value":"2014-11-13"},"_buckets":{"deposit":"d0b0edf0-fd2c-4d97-ab6a-785ac500f1aa"},"_deposit":{"id":"106920","pid":{"type":"depid","value":"106920","revision_id":0},"owners":[11],"status":"published","created_by":11},"item_title":"Approximating the Colorful Caratheodory Theorem","author_link":["14606","14605","14608","14607"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Approximating the Colorful Caratheodory Theorem"},{"subitem_title":"Approximating the Colorful Caratheodory Theorem","subitem_title_language":"en"}]},"item_type_id":"4","publish_date":"2014-11-13","item_4_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Institut fur Informatik, Freie Universitat Berlin"},{"subitem_text_value":"Institut fur Informatik, Freie Universitat Berlin"}]},"item_4_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Institut fur Informatik, Freie Universitat Berlin","subitem_text_language":"en"},{"subitem_text_value":"Institut fur Informatik, Freie Universitat Berlin","subitem_text_language":"en"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_publisher":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"情報処理学会","subitem_publisher_language":"ja"}]},"publish_status":"0","weko_shared_id":-1,"item_file_price":{"attribute_name":"Billing file","attribute_type":"file","attribute_value_mlt":[{"url":{"url":"https://ipsj.ixsq.nii.ac.jp/record/106920/files/IPSJ-AL14150028.pdf"},"date":[{"dateType":"Available","dateValue":"2016-11-13"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-AL14150028.pdf","filesize":[{"value":"1.1 MB"}],"mimetype":"application/pdf","priceinfo":[{"tax":["include_tax"],"price":"660","billingrole":"5"},{"tax":["include_tax"],"price":"330","billingrole":"6"},{"tax":["include_tax"],"price":"0","billingrole":"9"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"7d996db3-64b5-4f72-8427-4cfb3601d096","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2014 by the Information Processing Society of Japan"}]},"item_4_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Wolfgang, Mulzer"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Yannik, Stein"}],"nameIdentifiers":[{}]}]},"item_4_creator_6":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Wolfgang, Mulzer","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Yannik, Stein","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_4_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN1009593X","subitem_source_identifier_type":"NCID"}]},"item_4_textarea_12":{"attribute_name":"Notice","attribute_value_mlt":[{"subitem_textarea_value":"SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc."}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_18gh","resourcetype":"technical report"}]},"item_4_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"Let P1,..., Pd+1 ⊂ Rd be point sets whose convex hulls each contain the origin. Each set represents a color class. The Colorful Caratheodory theorem guarantees the existence of a colorful choice, i.e., a set that contains exactly one point from each color class, whose convex hull also contains the origin. So far, the computational complexity of computing such a colorful choice is unknown and thus approximation algorithms are of interest. We consider a new notion of approximation: a set C′ is called an m-colorful choice if it contains at most m points from each color class. We show that for all constant ε > 0, an ε(d+1)-colorful choice containing the origin in its convex hull can be found in polynomial time.","subitem_description_type":"Other"}]},"item_4_description_8":{"attribute_name":"論文抄録(英)","attribute_value_mlt":[{"subitem_description":"Let P1,..., Pd+1 ⊂ Rd be point sets whose convex hulls each contain the origin. Each set represents a color class. The Colorful Caratheodory theorem guarantees the existence of a colorful choice, i.e., a set that contains exactly one point from each color class, whose convex hull also contains the origin. So far, the computational complexity of computing such a colorful choice is unknown and thus approximation algorithms are of interest. We consider a new notion of approximation: a set C′ is called an m-colorful choice if it contains at most m points from each color class. We show that for all constant ε > 0, an ε(d+1)-colorful choice containing the origin in its convex hull can be found in polynomial time.","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"6","bibliographic_titles":[{"bibliographic_title":"研究報告アルゴリズム（AL）"}],"bibliographicPageStart":"1","bibliographicIssueDates":{"bibliographicIssueDate":"2014-11-13","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"28","bibliographicVolumeNumber":"2014-AL-150"}]},"relation_version_is_last":true,"weko_creator_id":"11"},"updated":"2025-01-21T09:14:27.593041+00:00","created":"2025-01-18T23:50:14.052857+00:00","id":106920}