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dc.contributorPerarnau Llobet, Guillem
dc.contributor.authorGonzález I Sentís, Marta
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.description.abstractGraph colouring is arguably one of the most important issues in Graph Theory. However, many of the questions that arise in the area such as the chromatic number problem or counting the number of proper colorings of a graph are known to be hard. This is the reason why approximation schemes are considered. In this thesis we consider the problem of approximate sampling a proper coloring at random. Among others, approximate samplers yield approximation schemes for the problem of counting the number of colourings of a graph. These samplers are based in Markov chains, and the main requirement of these chains is to mix rapidly, namely in time polynomial in the number of vertices. Two main examples are the Glauber and the flip dynamics. In the project we study under which conditions these chains mix rapidly and hence under which conditions there exist efficient samplers.
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subject.lcshCombinatorial analysis
dc.subject.otherGraph coloring
dc.subject.otherApproximate samplers
dc.subject.otherMarkov chains
dc.subject.otherRandomized algorithms
dc.titleApproximation schemes for randomly sampling colorings
dc.typeMaster thesis
dc.subject.lemacCombinacions (Matemàtica)
dc.subject.amsClassificació AMS::05 Combinatorics
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística

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