Fast algorithms to generate restricted classes of strings under rotation

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dc.contributor.author Sawada, Joseph James
dc.date.accessioned 2018-01-29T21:37:50Z
dc.date.available 2018-01-29T21:37:50Z
dc.date.copyright 2000 en_US
dc.date.issued 2018-01-29
dc.identifier.uri https://dspace.library.uvic.ca//handle/1828/9017
dc.description.abstract A 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.language English eng
dc.language.iso en en_US
dc.rights Available to the World Wide Web en_US
dc.subject Algorithms en_US
dc.subject Computer programming en_US
dc.title Fast algorithms to generate restricted classes of strings under rotation en_US
dc.type Thesis en_US
dc.contributor.supervisor Ruskey, Frank
dc.degree.department Department of Computer Science en_US
dc.degree.level Doctor of Philosophy Ph.D. en_US
dc.description.scholarlevel Graduate en_US

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