Fast algorithms to generate restricted classes of strings under rotation

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dc.contributor.authorSawada, Joseph James
dc.contributor.supervisorRuskey, Frank
dc.date.accessioned2018-01-29T21:37:50Z
dc.date.available2018-01-29T21:37:50Z
dc.date.copyright2000en_US
dc.date.issued2018-01-29
dc.degree.departmentDepartment of Computer Scienceen_US
dc.degree.levelDoctor of Philosophy Ph.D.en_US
dc.description.abstractA necklace is a representative of an equivalence class of k-ary strings under rotation. Efficient algorithms for generating (i.e., listing) necklaces have been known for some time. Many applications, however, require a restricted class of necklaces for which no efficient generation algorithm previously existed. This dissertation addresses this problem by developing fast algorithms to generate the following restricted classes of necklaces: (a) unlabeled necklaces, (b) fixed density necklaces, (c) necklaces where the number of each alphabet symbol is fixed, (d) chord diagrams, (e) necklaces which avoid a particular Lyndon substring, and (f) bracelets. An analysis for each algorithm (a), (b), (e), and (f) shows that the amount of computation is proportional to the number of strings produced. Experimental results give a strong indication that the algorithms for (c) and (d) also achieve this time bound. In addition, a new derivation of the known formula for counting chord diagrams is presented, along with a linear time algorithm to generate a basis for the n-th homogeneous component of the free Lie algebra.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/9017
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectAlgorithmsen_US
dc.subjectComputer programmingen_US
dc.titleFast algorithms to generate restricted classes of strings under rotationen_US
dc.typeThesisen_US

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