{"?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-DGXQ8KP6/8319215a-6106-4468-9a7b-e622c45398d8/PDF","dcterms:extent":"487 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DGXQ8KP6/7b5559e2-e5aa-4733-83dd-207361b48217/TEXT","dcterms:extent":"56 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-DGXQ8KP6","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":["Hellmuth, Marc","Imrich, Wilfried","Kupka, Tomas"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:9"},{"@xml:lang":"sl","#text":"str. 223-242"}],"dc:identifier":["COBISSID:17605721","ISSN:1855-3966","URN:URN:NBN:SI:doc-DGXQ8KP6"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"approximate product"},{"@xml:lang":"sl","#text":"aproksimativni produkt"},{"@xml:lang":"en","#text":"Cartesian product"},{"@xml:lang":"sl","#text":"grafovski sveženj"},{"@xml:lang":"en","#text":"graph bundle"},{"@xml:lang":"sl","#text":"kartezični produkt"},{"@xml:lang":"sl","#text":"kvazi produkt"},{"@xml:lang":"sl","#text":"parcialno zvezdni produkt"},{"@xml:lang":"en","#text":"partial star product"},{"@xml:lang":"en","#text":"product relation"},{"@xml:lang":"sl","#text":"produktna relacija"},{"@xml:lang":"en","#text":"quasi product"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Fast recognition of partial star products and quasi cartesian products|"},"dc:description":[{"@xml:lang":"sl","#text":"This paper is concerned with the fast computation of a relation ?$\\mathfrak{d}$? on the edge set of connected graphs that plays a decisive role in the recognition of approximate Cartesian products, the weak reconstruction of Cartesian products, and the recognition of Cartesian graph bundles with a triangle free basis. A special case of ?$\\mathfrak{d}$? is the relation ?$\\delta^\\ast$?, whose convex closure yields the product relation ?$\\delta$? that induces the prime factor decomposition of connected graphs with respect to the Cartesian product. For the construction of ?$\\mathfrak{d}$? so-called Partial Star Products are of particular interest. Several special data structures are used that allow to compute Partial Star Products in constant time. These computations are tuned to the recognition of approximate graph products, but also lead to a linear time algorithm for the computation of ?$\\delta^\\ast$? for graphs with maximum bounded degree. Furthermore, we define quasi Cartesian products as graphs with non-trivial ?$\\delta^\\ast$?. We provide several examples, and show that quasi Cartesian products can be recognized in linear time for graphs with bounded maximum degree. Finally, we note that quasi products can be recognized i n sublinear time with a parallelized algorithm"},{"@xml:lang":"sl","#text":"Članek obravnava hitro računanje relacije ?$\\mathfrak{d}$? na množici povezav povezanih grafov, ki igra odločilno vlogo pri prepoznavanju aproksimativnih kartezičnih produktov, pri šibki rekonstrukciji kartezičnih produktov in pri prepoznavanju svežnjev kartezičnega grafa z bazo brez trikotnikov. Poseben primer relacije ?$\\mathfrak{d}$? je relacija ?$\\delta^\\ast$?, katere konveksno zaprtje nam da produktno relacijo ?$\\delta$?, ki inducira prafaktorsko dekompozicijo povezanih grafov glede na kartezični produkt. Za konstrukcijo ?$\\mathfrak{d}$? so posebej zanimivi t.i. parcialni zvezdni produkti. Z uporabo različnih posebnih podatkovnih struktur lahko izračunamo parcialne zvezdne produkte v konstantnem času. Ti izračuni so uglašeni s prepoznavanjem aproksimativnih grafovskih produktov, vodijo pa tudi k algoritmu, ki v linearnem času izračuna ?$\\delta^\\ast$? za grafe z maksimalno omejeno stopnjo. Nadalje, definiramo kvazi kartezične produkte kot grafe z netirivialnim ?$\\delta^\\ast$?. Podamo več primerov in pokažemo, da lahko pri grafih z omejeno maksimalno stopnjo kvazi kartezične produkte prepoznamo v linearnem času. Nazadnje omenimo, da lahko kvazi produkte prepoznamo v sublinearnem času s paraleliziranim algoritmom"}],"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-DGXQ8KP6","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-DGXQ8KP6"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-DGXQ8KP6/8319215a-6106-4468-9a7b-e622c45398d8/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-DGXQ8KP6/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-DGXQ8KP6"}}}}