{"created":"2025-01-19T00:35:54.800194+00:00","updated":"2025-01-20T11:03:10.751608+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00164043","sets":["1164:2592:8452:8750"]},"path":["8750"],"owner":"11","recid":"164043","title":["距離限定部分グラフ探索問題に対する近似アルゴリズム"],"pubdate":{"attribute_name":"公開日","attribute_value":"2016-06-17"},"_buckets":{"deposit":"4af9c82c-8e90-4293-8505-a265aaf64779"},"_deposit":{"id":"164043","pid":{"type":"depid","value":"164043","revision_id":0},"owners":[11],"status":"published","created_by":11},"item_title":"距離限定部分グラフ探索問題に対する近似アルゴリズム","author_link":["322613","322607","322609","322610","322612","322606","322611","322608"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"距離限定部分グラフ探索問題に対する近似アルゴリズム"},{"subitem_title":"Approximation Algorithms for Maximum Distance-Bounded Subgraph Problems","subitem_title_language":"en"}]},"item_type_id":"4","publish_date":"2016-06-17","item_4_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"九州産業大学情報科学部"},{"subitem_text_value":"九州工業大学大学院情報工学研究院システム創成情報工学研究系"},{"subitem_text_value":"九州工業大学大学院情報工学研究院システム創成情報工学研究系"},{"subitem_text_value":"九州工業大学大学院情報工学研究院システム創成情報工学研究系"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"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/164043/files/IPSJ-AL16158018.pdf","label":"IPSJ-AL16158018.pdf"},"date":[{"dateType":"Available","dateValue":"2018-06-17"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-AL16158018.pdf","filesize":[{"value":"436.8 kB"}],"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":"d0b2c7a4-f83c-4afc-bb69-4168a5d0ba03","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2016 by the Information Processing Society of Japan"}]},"item_4_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"朝廣, 雄一"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"土井, 悠也"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"志水, 宏宇"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"宮野, 英次"}],"nameIdentifiers":[{}]}]},"item_4_creator_6":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Yuichi, Asahiro","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Yuya, Doi","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Hirotaka, Shimizu","creatorNameLang":"en"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Eiji, Miyano","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_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"2188-8566","subitem_source_identifier_type":"ISSN"}]},"item_4_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"グラフ G=(V,E) 中の頂点集合 S ⊆ V を考える．S 中の任意の頂点 u, v の組に対して，G 中での u と v の間の距離が高々 d である場合に S は d-クリークであると言う．また，S により誘導される G の部分グラフの直径が高々 d の場合には，S は d-クラブであると言う．与えられた n 頂点グラフに対して，Max d-Clique 問題 (または Max d-Club 問題) の目的は，G 中の最大 d-クリーク (または最大 d-クラブ) を発見することである．任意の ε>0 に対して，Max 1-Clique と Max 1-Club は，P = NP でない限り多項式時間で n1-ε- 近似できない．なぜならば，これらの問題は Max Clique と同じ問題であり，Max Clique が P = NP でない限り多項式時間で n1-ε- 近似できないからである ([5], [10])．さらに，任意の固定された d ≧ 2 と任意の ε > 0 に対して，Max d-Club は P = NP でない限り n1/2-ε- 近似できないことも知られている [2]．Max d-Club の近似上界に関しては，任意の偶数 d ≧ 2 に対する多項式時間 O(n1/2)- 近似アルゴリズムが著者らのグループにより提案されている [2]．しかしながら，奇数 d ≧ 3 に対しては，このアルゴリズムの近似率は O(n2/3) に悪化するため，近似下界 Ω(n1/2-ε) との乖離が依然として残っている [2]．本稿ではまず，Max d-Club の近似上界の改善を行う．すなわち，任意の奇数 d ≧ 3 に対して多項式時間 O(n1/2)- 近似アルゴリズムを提案する．そして同様のアイデアを用いて，任意の d ≧ 2 に対して Max d-Clique も多項式時間で O(n1/2)- 近似できることを示す．それとともに P = NP でない限り，任意の ε > 0 に対して，Max d-Clique も n1/2-ε- 近似できないことについて述べる．","subitem_description_type":"Other"}]},"item_4_description_8":{"attribute_name":"論文抄録(英)","attribute_value_mlt":[{"subitem_description":"A d-clique in a graph G = (V,E) is a subset S ⊆ V of vertices such that for pairs of vertices u, v ∈ S, the distance between u and v is at most d in G. A d-club in a graph G = (V,E) is a subset S0 ⊆ V of vertices that induces a subgraph of G of diameter at most d. Given a graph G with n vertices, the goal of Max d-Clique (Max d-Club, resp.) is to find a d-clique (d-club, resp.) of maximum cardinality in G. Max 1-Clique and Max 1-Club cannot be efficiently approximated within a factor of n1-ε for any ε > 0 unless P = NP since they are identical to Max Clique [5], [10]. Also, it is known [2] that it is NP-hard to approximate Max d-Club to within a factor of n1/2-ε for any fixed d ≧ 2 and for any ε > 0. As for approximability of Max d-Club, there exists a polynomial-time algorithm which achieves an optimal approximation ratio of O(n1/2) for any even d ≧ 2 [2]. For any odd d ≧ 3, however, there still remains a gap between the O(n2/3)-approximability and the Ω(n1/2-ε)-inapproximability for Max d-Club [2]. In this paper, we first strengthen the approximability result for Max d-Club; we design a polynomial-time algorithm which achieves an optimal approximation ratio of O(n1/2) for Max d-Club for any odd d ≧ 3. Then, by using the similar ideas, we show the O(n1/2)-approximation algorithm for Max d-Clique for any d ≧ 2. This is the best possible in polynomial time unless P = NP, as we can prove the Ω(n1/2-ε)-inapproximability.","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":"2016-06-17","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"18","bibliographicVolumeNumber":"2016-AL-158"}]},"relation_version_is_last":true,"weko_creator_id":"11"},"id":164043,"links":{}}