Star bi-coloring of bipartite graphs

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dc.contributor.authorHasan, Ahmed Shoeb Al
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorHossain, Shahadat
dc.date.accessioned2020-01-13T21:39:20Z
dc.date.available2020-01-13T21:39:20Z
dc.date.issued2019
dc.degree.levelMastersen_US
dc.description.abstractEvaluation of the Jacobian is the most computationally expensive operation while solving a non-linear system. Knowledge of the sparsity pattern in advance reduces the computational cost. Bi-directional partitioning to determine non-zeroes in the sparse matrix works better than unidirectional partitioning for dense rows and dense columns. We have developed a bidirectional coloring algorithm that determines all the non-zeroes of a sparse Jacobian matrix. Our algorithm is inspired by complete direct cover. Several numerical experiments have been carried out on standard data sets. Test results ensure that our proposed algorithm works better than existing algorithms. We have implemented our algorithm using the data structures and partitioning algorithms defined in software tool kit DSJM (Determine Sparse Jacobian Matrices). We have added new procedures in DSJM, which facilitates bi-directional partitioning.en_US
dc.identifier.urihttps://hdl.handle.net/10133/5656
dc.language.isoen_USen_US
dc.proquest.subjectComputer science [0984]en_US
dc.proquest.subjectMathematics [0405]en_US
dc.proquest.subjectComputer engineering [0464]en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Scienceen_US
dc.publisher.departmentDepartment of Mathematics & Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectBipartite graphsen_US
dc.subjectComputer algorithmsen_US
dc.subjectJacobiansen_US
dc.subjectMachine learningen_US
dc.titleStar bi-coloring of bipartite graphsen_US
dc.typeThesisen_US
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