{"?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-80QO6PXU/9382f88e-2bcb-4561-afce-7531a2bc940a/PDF","dcterms:extent":"356 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-80QO6PXU/2c0c65e6-844a-466e-9839-c69bd29ef778/TEXT","dcterms:extent":"41 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-80QO6PXU","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":["Gerbner, Dániel","Keszegh, Balázs","Pálvölgyi, Dömötör","Rote, Günter","Wiener, Gábor"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:12"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 301-314"}],"dc:identifier":["COBISSID:18165081","ISSN:1855-3966","URN:URN:NBN:SI:doc-80QO6PXU"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":{"@xml:lang":"sl","#text":"grafi"},"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Search for the end of a path in the d-dimensional grid and in other graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"We consider the worst-case query complexity of some variants of certain PPAD- complete search problems. Suppose we are given a graph ?$G$? and a vertex ?$s \\in V (G)$?. We denote the directed graph obtained from ?$G$? by directing all edges in both directions by ?$G'$?. ?$D$? is a directed subgraph of ?$G'$? which is unknown to us, except that it consists of vertex-disjoint directed paths and cycles and one of the paths originates in ?$s$?. Our goal is to find an endvertex of a path by using as few queries as possible. A query specifies a vertex ?$v \\in V (G)$?, and the answer is the set of the edges of ?$D$? incident to ?$v$?, together with their directions. We also show lower bounds for the special case when ?$D$? consists of a single path. Our proofs use the theory of graph separators. Finally, we consider the case when the graph ?$G$? is a grid graph. In this case, using the connection with separators, we give asymptotically tight bounds as a function of the size of the grid, if the dimension of the grid is considered as fixed. In order to do this, we prove a separator theorem about grid graphs, which is interesting on its own right"},{"@xml:lang":"sl","#text":"Obravnavamo najslabši primer iskalne kompleksnosti nekaterih različic določenih PPAD-polnih iskalnih problemov. Denimo da je dan graf ?$G$? in vozlišče ?$s \\in V (G)$?. Označimo usmerjeni graf dobljen iz grafa ?$G$? z usmeritvijo vseh povezav v obe smeri z ?$G'$?. ?$D$? je usmerjen podgraf grafa ?$G'$?, ki nam je neznan, vemo le, da sestoji iz vozliščno-disjunktnih usmerjenih poti in ciklov, in da se ena od poti začne v ?$s$?. Naš cilj je najti končno vozlišče poti, za to pa uporabiti kar se malo iskanj. Iskanje specificira vozlišče ?$v \\in V (G)$?, in odgovor je množica povezav grafa ?$D$? incidentnih vozlišču ?$v$?, skupaj z njihovimi smermi. Določimo tudi spodnje meje za posebni primer, ko ?$D$? sestoji iz ene same poti. Naši dokazi uporabljajo teorijo grafovskih ločevalcev. Nazadnje obravnavamo primer, ko je graf ?$G$? rešetkast graf. V tem primeru, uporabljajoč zvezo z ločevalci, podamo asimptotsko tesne meje, izražene z velikostjo rešetke, če je dimenzija rešetke smatrana za fiksno. V ta namen dokažemo ločevalske izreke v zvezi z rešetkastimi grafi, ki so zanimivi tudi sami po sebi"}],"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-80QO6PXU","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-80QO6PXU"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-80QO6PXU/9382f88e-2bcb-4561-afce-7531a2bc940a/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-80QO6PXU/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-80QO6PXU"}}}}