Computing all the simple symmetric monotone venn diagrams on seven curves

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dc.contributor.authorCao, Taoen_US
dc.date.accessioned2024-08-13T17:19:32Z
dc.date.available2024-08-13T17:19:32Z
dc.date.copyright2001en_US
dc.date.issued2001
dc.degree.departmentDepartment of Computer Science
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractA family of intersecting simple closed curves (FISC) 1s a collection of simple closed curves in the plane with the properties that there is some open region common to the interiors of all the curves, and that every two curves intersect in finitely many points. A normal FISC, or NFISC is a FISC with the properĀ­ ties that each curve touches the outer face and the family is convex-drawable. In this thesis, we present a G-encoding technique for an NFISC, which generĀ­alizes a Grunbaum encoding for a simple monotone Venn diagram. We prove that NFISC diagrams can be uniquely identified with their G-encodings, and simple monotone Venn diagrams can be identified with their Grunbaum encodings. By applying this theory, we develop two algorithms to search all possible simple symmetric monotone (SSM) Venn diagrams with seven curves.The total number of such diagrams is 23.
dc.format.extent77 pages
dc.identifier.urihttps://hdl.handle.net/1828/17388
dc.rightsAvailable to the World Wide Weben_US
dc.titleComputing all the simple symmetric monotone venn diagrams on seven curvesen_US
dc.typeThesisen_US

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