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dc.contributorDepartment of Computingen_US
dc.contributor.advisorCao, Yixin (COMP)en_US
dc.creatorKe, Yuping-
dc.publisherHong Kong Polytechnic Universityen_US
dc.rightsAll rights reserveden_US
dc.titleKernelization for edge modification problemsen_US
dcterms.abstractGraph modification problems are significant problems in computer science that have gained considerable attention in recent decades. In this thesis, we focus on edge modification problems, whose task is to make an input graph satisfy some required properties by making small changes to the edges in the graph.en_US
dcterms.abstractWe study kernelization algorithms for edge modification problems toward sev­eral graph classes that can be characterized by a finite set of forbidden induced sub­graphs and provide small kernels for these problems. A kernelization algorithm is a preprocessing algorithm that reduces the input instances to an equivalent instance with a smaller size in polynomial time. We show that the edge deletion problem toward cluster graphs and the edge addition problem toward paw-free graphs ad­mit linear kernels, a 2k-vertex kernel for the former one and a 38k-vertex kernel for the latter one. In addition, we prove that the edge addition problem toward triv­ially perfect graphs admits a quadratic kernel. We also prove that the edge addition problem and the edge deletion problem toward (pseudo-) split graphs have a kernel with O(K1.5) vertices.en_US
dcterms.extentx, 151 pages : color illustrationsen_US
dcterms.isPartOfPolyU Electronic Thesesen_US
dcterms.educationalLevelAll Doctorateen_US
dcterms.LCSHGraph theoryen_US
dcterms.LCSHGraph algorithmsen_US
dcterms.LCSHComputer algorithmsen_US
dcterms.LCSHHong Kong Polytechnic University -- Dissertationsen_US
dcterms.accessRightsopen accessen_US

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