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DOI: 10.4230/LIPIcs.ESA.2022.12

Computing NP-Hard Repetitiveness Measures via MAX-SAT

Authors: Hideo Bannai, Keisuke Goto, Masakazu Ishihata, Shunsuke Kanda, Dominik Köppl, and Takaaki Nishimoto

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract

Repetitiveness measures reveal profound characteristics of datasets, and give rise to compressed data structures and algorithms working in compressed space. Alas, the computation of some of these measures is NP-hard, and straight-forward computation is infeasible for datasets of even small sizes. Three such measures are the smallest size of a string attractor, the smallest size of a bidirectional macro scheme, and the smallest size of a straight-line program. While a vast variety of implementations for heuristically computing approximations exist, exact computation of these measures has received little to no attention. In this paper, we present MAX-SAT formulations that provide the first non-trivial implementations for exact computation of smallest string attractors, smallest bidirectional macro schemes, and smallest straight-line programs. Computational experiments show that our implementations work for texts of length up to a few hundred for straight-line programs and bidirectional macro schemes, and texts even over a million for string attractors.

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Hideo Bannai, Keisuke Goto, Masakazu Ishihata, Shunsuke Kanda, Dominik Köppl, and Takaaki Nishimoto. Computing NP-Hard Repetitiveness Measures via MAX-SAT. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bannai_et_al:LIPIcs.ESA.2022.12,
  author =	{Bannai, Hideo and Goto, Keisuke and Ishihata, Masakazu and Kanda, Shunsuke and K\"{o}ppl, Dominik and Nishimoto, Takaaki},
  title =	{{Computing NP-Hard Repetitiveness Measures via MAX-SAT}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.12},
  URN =		{urn:nbn:de:0030-drops-169505},
  doi =		{10.4230/LIPIcs.ESA.2022.12},
  annote =	{Keywords: repetitiveness measures, string attractor, bidirectional macro scheme}
}

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2022.99

An Optimal-Time RLBWT Construction in BWT-Runs Bounded Space

Authors: Takaaki Nishimoto, Shunsuke Kanda, and Yasuo Tabei

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract

The compression of highly repetitive strings (i.e., strings with many repetitions) has been a central research topic in string processing, and quite a few compression methods for these strings have been proposed thus far. Among them, an efficient compression format gathering increasing attention is the run-length Burrows-Wheeler transform (RLBWT), which is a run-length encoded BWT as a reversible permutation of an input string on the lexicographical order of suffixes. State-of-the-art construction algorithms of RLBWT have a serious issue with respect to (i) non-optimal computation time or (ii) a working space that is linearly proportional to the length of an input string. In this paper, we present r-comp, the first optimal-time construction algorithm of RLBWT in BWT-runs bounded space. That is, the computational complexity of r-comp is O(n + r log r) time and O(r log n) bits of working space for the length n of an input string and the number r of equal-letter runs in BWT. The computation time is optimal (i.e., O(n)) for strings with the property r = O(n/log n), which holds for most highly repetitive strings. Experiments using a real-world dataset of highly repetitive strings show the effectiveness of r-comp with respect to computation time and space.

Cite as

Takaaki Nishimoto, Shunsuke Kanda, and Yasuo Tabei. An Optimal-Time RLBWT Construction in BWT-Runs Bounded Space. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 99:1-99:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{nishimoto_et_al:LIPIcs.ICALP.2022.99,
  author =	{Nishimoto, Takaaki and Kanda, Shunsuke and Tabei, Yasuo},
  title =	{{An Optimal-Time RLBWT Construction in BWT-Runs Bounded Space}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{99:1--99:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.99},
  URN =		{urn:nbn:de:0030-drops-164403},
  doi =		{10.4230/LIPIcs.ICALP.2022.99},
  annote =	{Keywords: lossless data compression, Burrows-Wheeler transform, highly repetitive text collections}
}

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Computing NP-Hard Repetitiveness Measures via MAX-SAT

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An Optimal-Time RLBWT Construction in BWT-Runs Bounded Space

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