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DOI: 10.4230/LIPIcs.CPM.2026.34

LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access

Authors: Hiroki Shibata, Yuto Nakashima, Yutaro Yamaguchi, and Shunsuke Inenaga

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract

An LZ-like factorization of a string divides it into factors, each being either a single character or a copy of a preceding substring. While grammar-based compression schemes support efficient random access with space linear in the compressed size, no comparable guarantees are known for general LZ-like factorizations. This limitation motivated restricted variants such as LZ-End [Kreft and Navarro, 2013] and height-bounded LZ (LZHB) [Bannai et al., 2024], which trade off some compression efficiency for faster access. In this paper, we introduce LZ-Begin-End (LZBE), a new LZ-like variant in which every copy factor must refer to a contiguous sequence of preceding factors. This structural restriction ensures that any context-free grammar can be transformed into an LZBE factorization of the same size. We further study the greedy LZBE factorization, which selects each copy factor to be as long as possible while processing the input from left to right, and show that it can be computed in linear time. Moreover, we exhibit a family of strings for which the greedy LZBE factorization is asymptotically smaller than the smallest grammar. These results demonstrate that the LZBE scheme is strictly more expressive than grammar-based compression in the worst case. To support fast queries, we propose a data structure for LZBE-compressed strings that permits O(log n)-time random access within space linear in the compressed size, where n is the length of the input string.

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Hiroki Shibata, Yuto Nakashima, Yutaro Yamaguchi, and Shunsuke Inenaga. LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 34:1-34:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{shibata_et_al:LIPIcs.CPM.2026.34,
  author =	{Shibata, Hiroki and Nakashima, Yuto and Yamaguchi, Yutaro and Inenaga, Shunsuke},
  title =	{{LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{34:1--34:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.34},
  URN =		{urn:nbn:de:0030-drops-259609},
  doi =		{10.4230/LIPIcs.CPM.2026.34},
  annote =	{Keywords: data compression, Lempel-Ziv parsing, string algorithms, random access}
}

Document

DOI: 10.4230/LIPIcs.SEA.2025.12

Bit Packed Encodings for Grammar-Compressed Strings Supporting Fast Random Access

Authors: Alan M. Cleary, Joseph Winjum, Jordan Dood, Hiroki Shibata, and Shunsuke Inenaga

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract

Grammar-based compression is a powerful compression technique that allows for computation over the compressed data. While there has been extensive theoretical work on grammar and encoding size, there has been little work on practical grammar encodings. In this work, we consider the canonical array-of-arrays grammar representation and present a general bit packing approach for reducing its space requirements in practice. We then present three bit packing strategies based on this approach - one online and two offline - with different space-time trade-offs. This technique can be used to encode any grammar-compressed string while preserving the virtues of the array-of-arrays representation. We show that our encodings are Nlog₂ N away from the information-theoretic bound, where N is the number of symbols in the grammar, and that they are much smaller than methods that meet the information-theoretic bound in practice. Moreover, our experiments show that by using bit packed encodings we can achieve state-of-the-art performance both in grammar encoding size and run-time performance of random-access queries.

Cite as

Alan M. Cleary, Joseph Winjum, Jordan Dood, Hiroki Shibata, and Shunsuke Inenaga. Bit Packed Encodings for Grammar-Compressed Strings Supporting Fast Random Access. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cleary_et_al:LIPIcs.SEA.2025.12,
  author =	{Cleary, Alan M. and Winjum, Joseph and Dood, Jordan and Shibata, Hiroki and Inenaga, Shunsuke},
  title =	{{Bit Packed Encodings for Grammar-Compressed Strings Supporting Fast Random Access}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.12},
  URN =		{urn:nbn:de:0030-drops-232506},
  doi =		{10.4230/LIPIcs.SEA.2025.12},
  annote =	{Keywords: String algorithms, data compression, random access, grammar-based compression}
}

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Documents authored by Shibata, Hiroki

LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access

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Bit Packed Encodings for Grammar-Compressed Strings Supporting Fast Random Access

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