{"links":{},"id":2006437,"metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:02006437","sets":["1164:2592:1766466972379:1766467104470"]},"path":["1766467104470"],"owner":"80578","recid":"2006437","title":["有向頂点素パス問題に対する木幅をパラメータとするアルゴリズムと下界"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2026-01-06"},"_buckets":{"deposit":"9a7ebeff-ebf7-46a3-86aa-0d0269d4b5e8"},"_deposit":{"id":"2006437","pid":{"type":"depid","value":"2006437","revision_id":0},"owners":[80578],"status":"published","created_by":80578},"item_title":"有向頂点素パス問題に対する木幅をパラメータとするアルゴリズムと下界","author_link":[],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"有向頂点素パス問題に対する木幅をパラメータとするアルゴリズムと下界","subitem_title_language":"ja"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"AL16","subitem_subject_scheme":"Other"}]},"item_type_id":"4","publish_date":"2026-01-06","item_4_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"金沢大学大学院電子情報通信学専攻"},{"subitem_text_value":"金沢大学大学院電子情報通信学専攻"}]},"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/2006437/files/IPSJ-AL26206016.pdf","label":"IPSJ-AL26206016.pdf"},"date":[{"dateType":"Available","dateValue":"2028-01-06"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-AL26206016.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":"40d8aff5-2d77-4c94-966d-48cca977bc7f","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2026 by the Information Processing Society of Japan"}]},"item_4_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"DongYun,Byun"}]},{"creatorNames":[{"creatorName":"松林,昭"}]}]},"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":"k-頂点素パス問題は，n頂点グラフGとk組のGの頂点対(s1, t1), ..., (sk, tk)が与えられ，各1≤i≤kに対してsiとtiを結ぶ互いに頂点素なk本のパスがGに存在するか否かを問う問題である．Gが無向であるとき，この問題は定数のkに対しては多項式時間で解けるが，一般のkに対してはNP完全であり，様々なFPTアルゴリズムが研究されている．特にGの木幅twをパラメータとする22tw log tw+O(tw)・n時間アルゴリズムがScheffler (Technical Report 396, TU Berlin, '94)によって提案されており，また，指数時間仮説の下では，パス幅pwに対して2o(pw log pw)・n O(1)時間アルゴリズムが存在しないことがLokshtanovら(SIAM J. Comput. '18)によって示されている．本稿ではGが有向グラフである場合を考える．このときはk=2の場合でさえもNP完全であることが知られている．Lokshtanovらの下界はGが有向である場合にも成立するが，証明ではk=Ω(tw4)に設定されており，より小さいkに関してもこの下界が成立するか否かは不明であった．本研究では2O((tw+k)log k)・n時間アルゴリズムを提案し，k=two(1)であるような小さいkに対しては，Lokshtanovらの下界よりも高速なアルゴリズムが存在することを示す．さらに，強指数時間仮説の下では(2-ε)pw log pw・nO(1)時間アルゴリズムが存在しないことを証明するとともに，Schefflerのアルゴリズムが，僅かな変更によって，有向グラフ上で2pw log pw+O(pw)・n時間で動くことを述べ，証明した下界が最適であることを示す．","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"8","bibliographic_titles":[{"bibliographic_title":"研究報告アルゴリズム（AL）"}],"bibliographicPageStart":"1","bibliographicIssueDates":{"bibliographicIssueDate":"2026-01-06","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"16","bibliographicVolumeNumber":"2026-AL-206"}]},"relation_version_is_last":true,"weko_creator_id":"80578"},"created":"2025-12-23T06:08:20.881792+00:00","updated":"2025-12-23T06:08:25.425998+00:00"}