TY - JOUR

T1 - An efficient generalized shift-rule for the prefer-max De Bruijn sequence

AU - Amram, Gal

AU - Rubin, Amir

N1 - Publisher Copyright:
© 2019 Elsevier B.V.

PY - 2020/2

Y1 - 2020/2

N2 - One of the fundamental ways to construct De Bruijn sequences is by using a shift-rule. A shift-rule receives a word as an argument and computes the symbol that appears after it in the sequence. An optimal shift-rule for an (n,k)-De Bruijn sequence runs in time O(n). We propose an extended notion we name a generalized-shift-rule, which receives a word, w, and an integer, c, and outputs the c symbols that comes after w. An optimal generalized-shift-rule for an (n,k)-De Bruijn sequence runs in time O(n+c). We show that, unlike in the case of a shift-rule, a time optimal generalized-shift-rule allows to construct the entire sequence efficiently. We provide a time optimal generalized-shift-rule for the well-known prefer-max and prefer-min De Bruijn sequences.

AB - One of the fundamental ways to construct De Bruijn sequences is by using a shift-rule. A shift-rule receives a word as an argument and computes the symbol that appears after it in the sequence. An optimal shift-rule for an (n,k)-De Bruijn sequence runs in time O(n). We propose an extended notion we name a generalized-shift-rule, which receives a word, w, and an integer, c, and outputs the c symbols that comes after w. An optimal generalized-shift-rule for an (n,k)-De Bruijn sequence runs in time O(n+c). We show that, unlike in the case of a shift-rule, a time optimal generalized-shift-rule allows to construct the entire sequence efficiently. We provide a time optimal generalized-shift-rule for the well-known prefer-max and prefer-min De Bruijn sequences.

KW - De Bruijn sequence

KW - Ford sequence

KW - Prefer-max sequence

KW - Shift rule

UR - http://www.scopus.com/inward/record.url?scp=85075332217&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2019.111657

DO - 10.1016/j.disc.2019.111657

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AN - SCOPUS:85075332217

SN - 0012-365X

VL - 343

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

M1 - 111657

ER -