A surprisingly simple de Bruijn sequence construction

Joe Sawada; Aaron Williams; Dennis Wong

doi:10.1016/j.disc.2015.08.002

A surprisingly simple de Bruijn sequence construction

Joe Sawada, Aaron Williams, Dennis Wong

Research output: Contribution to journal › Article › peer-review

40 Citations (Scopus)

Abstract

Pick any length n binary string ^b1^b2⋯^bn and remove the first bit ^b1. If ^b2^b3⋯^bn1 is a necklace, then append the complement of ^b1 to the end of the remaining string; otherwise append ^b1. By repeating this process, eventually all 2ⁿ binary strings will be visited cyclically. This shift rule leads to a new de Bruijn sequence construction that can be generated in O(1)-amortized time per bit.

Original language	English
Pages (from-to)	127-131
Number of pages	5
Journal	Discrete Mathematics
Volume	339
Issue number	1
DOIs	https://doi.org/10.1016/j.disc.2015.08.002
Publication status	Published - 6 Jan 2016
Externally published	Yes

Keywords

CAT algorithm
De Bruijn sequence
Generate
Necklaces
Shift Gray code
Shift rule
Successor rule
Universal cycle

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10.1016/j.disc.2015.08.002

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KW - Necklaces

KW - Shift Gray code

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KW - Successor rule

KW - Universal cycle

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A surprisingly simple de Bruijn sequence construction

Abstract

Keywords

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