{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-HBUXQVS6/E6D29F64-12AE-4566-B5D2-4071B8631D00/PDF","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-HBUXQVS6/4f92e2e8-ced4-4689-8e7f-2a0ad6ad7913/PDF","dcterms:extent":"308 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-HBUXQVS6/813d117f-f37b-48cb-8511-94c3affc2487/TEXT","dcterms:extent":"23 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-HBUXQVS6","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2013","dc:creator":["DeLaVina, Ermelinda","Larson, Craig Erik"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:6"},{"@xml:lang":"sl","#text":"str. 237-245"}],"dc:identifier":["COBISSID:16473945","ISSN:1855-3966","URN:URN:NBN:SI:doc-HBUXQVS6"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"critical independence number"},{"@xml:lang":"en","#text":"critical independent set"},{"@xml:lang":"en","#text":"graph theory"},{"@xml:lang":"en","#text":"independence number"},{"@xml:lang":"en","#text":"König-Egerváry graph"},{"@xml:lang":"en","#text":"matching number"},{"@xml:lang":"sl","#text":"teorija grafov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"A parallel algorithm for computing the critical independence number and related sets|"},"dc:description":{"@xml:lang":"sl","#text":"An independent set ?$I_c$? is a critical independent set if ?$|I_c| - |N(I_c)| \\ge |J| - |N(J)|$?, for any independent set ?$J$?. The critical independence number of a graph is the cardinality of a maximum critical independent set. This number is a lower bound for the independence number and can be computed in polynomial-time. The existing algorithm runs in ?${\\mathcal O}\\left( n^{2.5}\\sqrt{(m/\\log n}\\right)$? time for a graph ?$G$? with ?$n = |V(G)|$? vertices and ?$m$? edges. It is demonstrated here that there is a parallel algorithm using ?$n$? processors that runs in ?${\\mathcal O}\\left( n^{1.5} \\sqrt{(m/\\log n}\\right)$? time. The new algorithm returns the union of all maximum critical independent sets. The graph induced on this set is a König-Egerváry graph whose components are either isolated vertices or which have perfect matchings"},"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-HBUXQVS6","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-HBUXQVS6"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-HBUXQVS6/E6D29F64-12AE-4566-B5D2-4071B8631D00/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-HBUXQVS6/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-HBUXQVS6"}}}}