dc.contributor.author Vergara, John Paul C. en dc.date.accessioned 2014-03-14T20:21:37Z en dc.date.available 2014-03-14T20:21:37Z en dc.date.issued 1997-04-08 en dc.identifier.other etd-3156151139751001 en dc.identifier.uri http://hdl.handle.net/10919/30401 en dc.description.abstract Let P be a predicate applicable to permutations. A permutation that satisfies P is called a generator. Given a permutation \$pi\$, MinSort_P is the problem of finding a shortest sequence of generators that, when composed with \$pi\$, yields the identity permutation. The length of this sequence is called the P distance of \$pi\$. Diam_P is the problem of finding the longest such distance for permutations of a given length. MinSort_P and Diam_P, for some choices of P, have applications in the study of genome rearrangements and in the design of interconnection networks. This dissertation considers generators that are swaps, reversals, or block-moves. Distance bounds on these generators are introduced and the corresponding problems are investigated. Reduction results, graph-theoretic models, exact and approximation algorithms, and heuristics for these problems are presented. Experimental results on the heuristics are also provided. When the bound is a function of the length of the permutation, there are several sorting problems such as sorting by block-moves and sorting by reversals whose bounded variants are at least as difficult as the corresponding unbounded problems. For some bounded problems, a strong relationship exists between finding optimal sorting sequences and correcting the relative order of individual pairs of elements. This fact is used in investigating MinSort_P and Diam_P for two particular predicates. A short block-move is a generator that moves an element at most two positions away from its original position. Sorting by short block-moves is solvable in polynomial time for two large classes of permutations: woven bitonic permutations and woven double-strip permutations. For general permutations, a polynomial-time (4/3)-approximation algorithm that computes short block-move distance is devised. The short block-move diameter for length-n permutations is determined. A short swap is a generator that swaps two elements that have at most one element between them. A polynomial-time 2-approximation algorithm for computing short swap distance is devised and a class of permutations where the algorithm computes the exact short swap distance is determined. Bounds for the short swap diameter for length-n permutations are determined. en dc.publisher Virginia Tech en dc.relation.haspart etd.pdf en dc.relation.haspart diss.pdf en dc.rights In Copyright en dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ en dc.subject none en dc.title Sorting by Bounded Permutations en dc.type Dissertation en dc.contributor.department Computer Science en dc.description.degree Ph. D. en thesis.degree.name Ph. D. en thesis.degree.level doctoral en thesis.degree.grantor Virginia Polytechnic Institute and State University en thesis.degree.discipline Computer Science en dc.contributor.committeechair Heath, Lenwood S. en dc.contributor.committeemember Allison, Donald C. S. en dc.contributor.committeemember Green, Edward L. en dc.contributor.committeemember Brown, Ezra A. en dc.contributor.committeemember Shaffer, Clifford A. en dc.identifier.sourceurl http://scholar.lib.vt.edu/theses/available/etd-3156151139751001/ en dc.date.sdate 1998-07-12 en dc.date.rdate 1997-04-08 en dc.date.adate 1997-04-08 en
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