The Binary String-to-String Correction Problem

dc.contributor.authorSpreen, Thomas D.
dc.contributor.supervisorRuskey, Frank
dc.contributor.supervisorStege, Ulrike
dc.date.accessioned2013-08-30T20:13:39Z
dc.date.available2013-08-30T20:13:39Z
dc.date.copyright2013en_US
dc.date.issued2013-08-30
dc.degree.departmentDept. of Computer Scienceen_US
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractString-to-String Correction is the process of transforming some mutable string M into an exact copy of some other string (the target string T), using a shortest sequence of well-defined edit operations. The formal STRING-TO-STRING CORRECTION problem asks for the optimal solution using just two operations: symbol deletion, and swap of adjacent symbols. String correction problems using only swaps and deletions are computationally interesting; in his paper On the Complexity of the Extended String-to-String Correction Problem (1975), Robert Wagner proved that the String-to-String Correction problem under swap and deletion operations only is NP-complete for unbounded alphabets. In this thesis, we present the first careful examination of the binary-alphabet case, which we call Binary String-to-String Correction (BSSC). We present several special cases of BSSC for which an optimal solution can be found in polynomial time; in particular, the case where T and M have an equal number of occurrences of a given symbol has a polynomial-time solution. As well, we demonstrate and prove several properties of BSSC, some of which do not necessarily hold in the case of String-to-String Correction. For instance: that the order of operations is irrelevant; that symbols in the mutable string, if swapped, will only ever swap in one direction; that the length of the Longest Common Subsequence (LCS) of the two strings is monotone nondecreasing during the execution of an optimal solution; and that there exists no correlation between the effect of a swap or delete operation on LCS, and the optimality of that operation. About a dozen other results that are applicable to Binary String-to-String Correction will also be presented.en_US
dc.description.proquestcode0984en_US
dc.description.proquestcode0715en_US
dc.description.proquestemailtspreen@gmail.comen_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/4884
dc.languageEnglisheng
dc.language.isoenen_US
dc.rights.tempAvailable to the World Wide Weben_US
dc.subjecttransportation problemen_US
dc.subjectnp-harden_US
dc.subjectswapen_US
dc.subjectdeletionen_US
dc.subjectbinary stringen_US
dc.subjectIversonianen_US
dc.subjecttarget stringen_US
dc.subjectmutable stringen_US
dc.subjectlongest common subsequenceen_US
dc.subjectlcsen_US
dc.subjectbinary string-to-string correctionen_US
dc.titleThe Binary String-to-String Correction Problemen_US
dc.typeThesisen_US

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