On greedy algorithms for binary de Bruijn sequences
We propose a general greedy algorithm for binary de Bruijn sequences, called Generalized Prefer-Opposite Algorithm, and its modifications. By identifying specific feedback functions and initial states, we demonstrate that most previously-known greedy algorithms that generate binary de Bruijn sequenc...
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| Published in | Applicable algebra in engineering, communication and computing Vol. 33; no. 5; pp. 523 - 550 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.11.2022
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0938-1279 1432-0622 |
| DOI | 10.1007/s00200-020-00459-3 |
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| Abstract | We propose a general greedy algorithm for binary de Bruijn sequences, called Generalized Prefer-Opposite Algorithm, and its modifications. By identifying specific feedback functions and initial states, we demonstrate that most previously-known greedy algorithms that generate binary de Bruijn sequences are particular cases of our algorithm. |
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| AbstractList | We propose a general greedy algorithm for binary de Bruijn sequences, called Generalized Prefer-Opposite Algorithm, and its modifications. By identifying specific feedback functions and initial states, we demonstrate that most previously-known greedy algorithms that generate binary de Bruijn sequences are particular cases of our algorithm. |
| Author | Ezerman, Martianus Frederic Chang, Zuling Fahreza, Adamas Aqsa |
| Author_xml | – sequence: 1 givenname: Zuling surname: Chang fullname: Chang, Zuling organization: School of Mathematics and Statistics, Zhengzhou University – sequence: 2 givenname: Martianus Frederic surname: Ezerman fullname: Ezerman, Martianus Frederic email: fredezerman@ntu.edu.sg organization: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University – sequence: 3 givenname: Adamas Aqsa surname: Fahreza fullname: Fahreza, Adamas Aqsa organization: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University |
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| Keywords | 11B50 de Bruijn sequence Binary periodic sequence Greedy algorithm Feedback function State graph 94A60 94A55 |
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| References_xml | – volume: 117 start-page: 728 issue: 8 year: 2010 end-page: 732 ident: CR15 article-title: A simple combinatorial algorithm for de Bruijn sequences publication-title: Am. Math. Mon. doi: 10.4169/000298910x515794 – volume: 55 start-page: 131 issue: 3 year: 1982 end-page: 143 ident: CR5 article-title: De Bruijn sequences—a model example of the interaction of discrete mathematics and computer science publication-title: Math. Mag. – year: 2001 ident: CR18 publication-title: Graph Theory – volume: 40 start-page: 859 issue: 12 year: 1934 end-page: 865 ident: CR19 article-title: A problem in arrangements publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0002-9904-1934-05988-3 – volume: 72 start-page: 1 year: 2018 end-page: 11 ident: CR9 article-title: Constructing de Bruijn sequences with co-lexicographic order: the -ary grandmama sequence publication-title: Eur. J. 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| SubjectTerms | Artificial Intelligence Computer Hardware Computer Science Greedy algorithms Original Paper Symbolic and Algebraic Manipulation Theory of Computation |
| Title | On greedy algorithms for binary de Bruijn sequences |
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