Double Eulerian cycles on de Bruijn digraphs
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Authors
Krahn, Gary William
Subjects
NA
Advisors
Fredricksen, Harold
Date of Issue
1994-06
Date
June 1994
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
A binary de Bruijn sequence has the property that every n-tuple is distinct on a given period of length 2". An efficient algorithm to generate a class of classi- cal de Bruijn sequences is given based upon the distance between cycles within the Good - de Bruijn digraph. The de Bruijn property on binary sequences is shown to be a randomness property of the ZERO and ONE run sequences. Utilizing this randomness we find additional new structure in de Bruijn sequences. We analyze binary sequences that are not de Bruijn but instead possess the sufficient structure so that every distinct binary n-tuple can be systematically "combed" out of the se- quence. These complete or nonclassical de Bruijn sequences are a generalization of the well-known de Bruijn cycle. Our investigation focuses on binary sequences, called double Eulerian cycles, that define a cycle along a graph (digraph) visiting each edge (arc) exactly twice. A new algorithm to generate a class of double Eulerian cycles on graphs and digraphs is found. Double Eulerian cycles along the binary Good - de Bruijn digraph are partitioned by the run structure of their defining sequences. This partition allows for a statistical analysis to determine the relative size of the set of complete cycles defined by the sequences we study. A measure that categorizes double Eulerian cycles along graphs (digraphs) by the distance between the two visitations of each edge (arc) is provided. An algorithm to generate double Eulerian cycles of minimum measure is given.
Type
Thesis
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Format
129 p.
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.