2 Search Results for "Sawada, Joe"

Document
DOI: 10.4230/LIPIcs.CPM.2022.9
Arbitrary-Length Analogs to de Bruijn Sequences

Authors: Abhinav Nellore and Rachel Ward

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
Let α̃ be a length-L cyclic sequence of characters from a size-K alphabet 𝒜 such that for every positive integer m ≤ L, the number of occurrences of any length-m string on 𝒜 as a substring of α̃ is ⌊ L / K^m ⌋ or ⌈ L / K^m ⌉. When L = K^N for any positive integer N, α̃ is a de Bruijn sequence of order N, and when L ≠ K^N, α̃ shares many properties with de Bruijn sequences. We describe an algorithm that outputs some α̃ for any combination of K ≥ 2 and L ≥ 1 in O(L) time using O(L log K) space. This algorithm extends Lempel’s recursive construction of a binary de Bruijn sequence. An implementation written in Python is available at https://github.com/nelloreward/pkl.
Cite as

Abhinav Nellore and Rachel Ward. Arbitrary-Length Analogs to de Bruijn Sequences. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{nellore_et_al:LIPIcs.CPM.2022.9,
  author =	{Nellore, Abhinav and Ward, Rachel},
  title =	{{Arbitrary-Length Analogs to de Bruijn Sequences}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.9},
  URN =		{urn:nbn:de:0030-drops-161361},
  doi =		{10.4230/LIPIcs.CPM.2022.9},
  annote =	{Keywords: de Bruijn sequence, de Bruijn word, Lempel’s D-morphism, Lempel’s homomorphism}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.66
Gray Codes and Symmetric Chains

Authors: Petr Gregor, Sven Jäger, Torsten Mütze, Joe Sawada, and Kaja Wille

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We consider the problem of constructing a cyclic listing of all bitstrings of length 2n+1 with Hamming weights in the interval [n+1-l,n+l], where 1 <= l <= n+1, by flipping a single bit in each step. This is a far-ranging generalization of the well-known middle two levels problem (l=1). We provide a solution for the case l=2 and solve a relaxed version of the problem for general values of l, by constructing cycle factors for those instances. Our proof uses symmetric chain decompositions of the hypercube, a concept known from the theory of posets, and we present several new constructions of such decompositions. In particular, we construct four pairwise edge-disjoint symmetric chain decompositions of the n-dimensional hypercube for any n >= 12.
Cite as

Petr Gregor, Sven Jäger, Torsten Mütze, Joe Sawada, and Kaja Wille. Gray Codes and Symmetric Chains. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 66:1-66:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{gregor_et_al:LIPIcs.ICALP.2018.66,
  author =	{Gregor, Petr and J\"{a}ger, Sven and M\"{u}tze, Torsten and Sawada, Joe and Wille, Kaja},
  title =	{{Gray Codes and Symmetric Chains}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{66:1--66:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.66},
  URN =		{urn:nbn:de:0030-drops-90703},
  doi =		{10.4230/LIPIcs.ICALP.2018.66},
  annote =	{Keywords: Gray code, Hamilton cycle, hypercube, poset, symmetric chain}
}
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