{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1390282679356399488.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1587/transinf.e96.d.443"}},{"identifier":{"@type":"HDL","@value":"http://hdl.handle.net/10228/0002000071"}},{"identifier":{"@type":"URI","@value":"https://kyutech.repo.nii.ac.jp/records/2000071"}},{"identifier":{"@type":"URI","@value":"https://www.jstage.jst.go.jp/article/transinf/E96.D/3/E96.D_443/_pdf"}},{"identifier":{"@type":"NAID","@value":"10031167429"}}],"resourceType":"学術雑誌論文(journal article)","dc:title":[{"@language":"en","@value":"Inapproximability of Maximum <i>r</i>-Regular Induced Connected Subgraph Problems"},{"@value":"Inapproximability of maximum r-regular induced connected subgraph problems"}],"dc:language":"en","description":[{"type":"abstract","notation":[{"@language":"en","@value":"Given a connected graph <i>G</i> = (<i>V</i>,<i>E</i>) on <i>n</i> vertices, the Maximum <i>r</i>-Regular Induced Connected Subgraph (<i>r</i>-MaxRICS) problem asks for a maximum sized subset of vertices <i>S ⊆ V</i> such that the induced subgraph <i>G</i>[<i>S</i>] on <i>S</i> is connected and <i>r</i>-regular. It is known that 2-MaxRICS and 3-MaxRICS are <i>NP</i>-hard. Moreover, 2-MaxRICS cannot be approximated within a factor of <i>n</i><sup>1-<i>ε</i></sup> in polynomial time for any <i>ε</i> > 0 unless <i>P</i> = <i>NP</i>. In this paper, we show that <i>r</i>-MaxRICS are <i>NP</i>-hard for any fixed integer <i>r</i> ≥ 4. Furthermore, we show that for any fixed integer <i>r</i> ≥ 3, <i>r</i>-MaxRICS cannot be approximated within a factor of <i>n</i><sup>1/6-<i>ε</i></sup> in polynomial time for any <i>ε</i> > 0 unless <i>P</i> = <i>NP</i>."}],"abstractLicenseFlag":"disallow"}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1420845751150447616","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"40304761"},{"@type":"NRID","@value":"1000040304761"},{"@type":"NRID","@value":"9000107358849"},{"@type":"NRID","@value":"9000347208017"},{"@type":"NRID","@value":"9000347207961"},{"@type":"NRID","@value":"9000259337825"},{"@type":"NRID","@value":"9000258456155"},{"@type":"NRID","@value":"9000258456164"},{"@type":"NRID","@value":"9000347210160"},{"@type":"NRID","@value":"9000258449916"},{"@type":"NRID","@value":"9000258458316"},{"@type":"NRID","@value":"9000241869931"},{"@type":"NRID","@value":"9000016836474"},{"@type":"NRID","@value":"9000347210162"},{"@type":"NRID","@value":"9000410649397"},{"@type":"NRID","@value":"9000403556663"},{"@type":"NRID","@value":"9000404099508"},{"@type":"NRID","@value":"9000283829593"},{"@type":"NRID","@value":"9000260207015"},{"@type":"NRID","@value":"9000408906748"},{"@type":"NRID","@value":"9000347208021"},{"@type":"NRID","@value":"9000403559838"},{"@type":"NRID","@value":"9000258455215"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/read0099903"}],"foaf:name":[{"@language":"en","@value":"ASAHIRO Yuichi"}],"jpcoar:affiliationName":[{"@language":"en","@value":"Department of Information Science, Kyushu Sangyo University"}]},{"@id":"https://cir.nii.ac.jp/crid/1420845751165635968","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"70794022"},{"@type":"NRID","@value":"1000070794022"},{"@type":"NRID","@value":"9000259337826"},{"@type":"NRID","@value":"9000241869933"},{"@type":"NRID","@value":"9000018750365"},{"@type":"NRID","@value":"9000383088088"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/hiroshi_eto"}],"foaf:name":[{"@language":"en","@value":"ETO Hiroshi"}],"jpcoar:affiliationName":[{"@language":"en","@value":"Department of System Design and Informatics, Kyushu Institute of Technology"}]},{"@id":"https://cir.nii.ac.jp/crid/1420564276170384768","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"10284548"},{"@type":"NRID","@value":"1000010284548"},{"@type":"NRID","@value":"9000347208019"},{"@type":"NRID","@value":"9000347207962"},{"@type":"NRID","@value":"9000324992921"},{"@type":"NRID","@value":"9000259337827"},{"@type":"NRID","@value":"9000403585997"},{"@type":"NRID","@value":"9000380483823"},{"@type":"NRID","@value":"9000004806893"},{"@type":"NRID","@value":"9000347210161"},{"@type":"NRID","@value":"9000410925148"},{"@type":"NRID","@value":"9000403586003"},{"@type":"NRID","@value":"9000347210158"},{"@type":"NRID","@value":"9000380482859"},{"@type":"NRID","@value":"9000004798235"},{"@type":"NRID","@value":"9000016492846"},{"@type":"NRID","@value":"9000347210165"},{"@type":"NRID","@value":"9000017682013"},{"@type":"NRID","@value":"9000410649398"},{"@type":"NRID","@value":"9000403147616"},{"@type":"NRID","@value":"9000403556664"},{"@type":"NRID","@value":"9000356885061"},{"@type":"NRID","@value":"9000383088090"},{"@type":"NRID","@value":"9000283829590"},{"@type":"NRID","@value":"9000404099511"},{"@type":"NRID","@value":"9000283829589"},{"@type":"NRID","@value":"9000410315824"},{"@type":"NRID","@value":"9000283829594"},{"@type":"NRID","@value":"9000347207950"},{"@type":"NRID","@value":"9000311056055"},{"@type":"NRID","@value":"9000260207016"},{"@type":"NRID","@value":"9000020035179"},{"@type":"NRID","@value":"9000408906750"},{"@type":"NRID","@value":"9000410922090"},{"@type":"NRID","@value":"9000347208022"},{"@type":"NRID","@value":"9000317124405"},{"@type":"NRID","@value":"9000403559840"},{"@type":"NRID","@value":"9000403152897"},{"@type":"NRID","@value":"9000403586009"},{"@type":"NRID","@value":"9000283829587"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/eijimiyano"}],"foaf:name":[{"@language":"en","@value":"MIYANO Eiji"}],"jpcoar:affiliationName":[{"@language":"en","@value":"Department of System Design and Informatics, Kyushu Institute of Technology"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"09168532"},{"@type":"EISSN","@value":"17451361"},{"@type":"NCID","@value":"AA10826272"}],"prism:publicationName":[{"@language":"en","@value":"IEICE Transactions on Information and Systems"},{"@language":"en","@value":"IEICE Trans. Inf. & Syst."}],"dc:publisher":[{"@language":"en","@value":"The Institute of Electronics, Information and Communication Engineers"},{"@language":"ja","@value":"一般社団法人 電子情報通信学会"}],"prism:publicationDate":"2013","prism:volume":"E96.D","prism:number":"3","prism:startingPage":"443","prism:endingPage":"449"},"reviewed":"false","dcterms:accessRights":"http://purl.org/coar/access_right/c_abf2","url":[{"@id":"https://kyutech.repo.nii.ac.jp/records/2000071"},{"@id":"https://www.jstage.jst.go.jp/article/transinf/E96.D/3/E96.D_443/_pdf"}],"availableAt":"2013","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=induced%20connected%20subgraph","dc:title":"induced connected subgraph"},{"@id":"https://cir.nii.ac.jp/all?q=regularity","dc:title":"regularity"},{"@id":"https://cir.nii.ac.jp/all?q=%3Ci%3ENP%3C/i%3E-hardness","dc:title":"<i>NP</i>-hardness"},{"@id":"https://cir.nii.ac.jp/all?q=inapproximability","dc:title":"inapproximability"}],"dcterms:subject":[{"subjectScheme":"Other","notation":[{"@value":"induced connected subgraph"}]},{"subjectScheme":"Other","notation":[{"@value":"regularity"}]},{"subjectScheme":"Other","notation":[{"@value":"NP-hardness"}]},{"subjectScheme":"Other","notation":[{"@value":"inapproximability"}]}],"project":[{"@id":"https://cir.nii.ac.jp/crid/1040000782131288320","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"22700019"},{"@type":"JGN","@value":"JP22700019"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22700019/"}],"notation":[{"@language":"ja","@value":"ウォークに基づく局所演算の結合による大域的最適化"},{"@language":"en","@value":"Global optimization by local optimization with 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