148 Search Results for "Sadakane, Kunihiko"

Volume

LIPIcs, Volume 212

32nd International Symposium on Algorithms and Computation (ISAAC 2021)

ISAAC 2021, December 6-8, 2021, Fukuoka, Japan

Editors: Hee-Kap Ahn and Kunihiko Sadakane

Document
DOI: 10.4230/LIPIcs.SEA.2026.13
Practical Parallel Block Tree Construction

Authors: Robert Clausecker, Florian Kurpicz, and Etienne Palanga

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
The block tree [Belazzougui et al., J. Comput. Syst. Sci. '21] is a compressed representation of a length-n text that supports access, rank, and select queries while requiring only O(z log n/z) words of space, where z is the number of Lempel-Ziv factors of the text. In other words, its space requirements are asymptotically comparable to those of the compressed text itself. In practice, block trees offer query performance comparable to that of state-of-the-art compressed rank and select indices. However, their construction is significantly slower, and the fastest known construction algorithms additionally require a significant amount of working memory. To address these limitations, we propose fast and lightweight parallel algorithms for the efficient construction of block trees. Our algorithm achieves similar construction speed than the currently fastest block tree construction algorithm on a single core and is up to eight times faster using 64 cores, while requiring an order of magnitude less memory. Overall, we achieve a speedup of up to 15.5 on 64 cores, which is in line with the parallel construction of the Lempel-Ziv compression.
Cite as

Robert Clausecker, Florian Kurpicz, and Etienne Palanga. Practical Parallel Block Tree Construction. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{clausecker_et_al:LIPIcs.SEA.2026.13,
  author =	{Clausecker, Robert and Kurpicz, Florian and Palanga, Etienne},
  title =	{{Practical Parallel Block Tree Construction}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.13},
  URN =		{urn:nbn:de:0030-drops-260175},
  doi =		{10.4230/LIPIcs.SEA.2026.13},
  annote =	{Keywords: block tree, shared memory, compression, SIMD, Karp-Rabin fingerprints}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.7
From Relative Compression to Hierarchical Compression

Authors: Philip Bille, Inge Li Gørtz, and Máximo Pérez-López

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
We introduce a framework to use any relative compression algorithm as a subroutine for hierarchical relative compression. In a dataset consisting of n sequences, it consists of constructing a rooted tree on the sequences, using hashing and similarity techniques, and compressing the children of a node relative to their parent. We build up on previous techniques [Bille et al., 2023], and optimize them further for computational efficiency. We test our framework with three existing relative compression algorithms on six genomic datasets, and we show that in datasets that contain heterogeneous data, hierarchical relative compression improves the compression ratio by a factor 2 or more, when compared to relative compression to a single sequence. Apart from compression ratio, we also explore the trade-offs with respect to compression speed, dataset decompression speed, and average sequence decompression speed. With two of the surveyed algorithms, dataset decompression becomes faster and sequence decompression remains practical, at the cost of compression time, which remains competitive for the datasets with highest variability.
Cite as

Philip Bille, Inge Li Gørtz, and Máximo Pérez-López. From Relative Compression to Hierarchical Compression. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bille_et_al:LIPIcs.SEA.2026.7,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and P\'{e}rez-L\'{o}pez, M\'{a}ximo},
  title =	{{From Relative Compression to Hierarchical Compression}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.7},
  URN =		{urn:nbn:de:0030-drops-260117},
  doi =		{10.4230/LIPIcs.SEA.2026.7},
  annote =	{Keywords: Relative compression, RLZ, string collections, compressed representation, data structures, efficient algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.10
Compressing Highly Repetitive Binary Trees with an Application to Range Minimum Queries

Authors: Gabriel Carmona and Filippo Lari

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
Tree compression is a well-studied area that aims at reducing the size of tree representations by exploiting different forms of repetition. While the underlying theory is well understood, there is still significant room for experimental investigation, particularly in the design of compressed representations that efficiently support navigational queries. In this work, we address the problem of designing, engineering, and experimentally evaluating a compression technique for unlabeled binary trees based on repeated subtrees, yielding the minimal Directed Acyclic Graph (DAG) of the input tree. We show how this representation can be computed in linear time and space directly from a succinct encoding of the tree, and how it can be augmented with compact auxiliary data structures to support Lowest Common Ancestor (LCA) queries. When the input tree is the Cartesian tree of an array, LCA queries can be used to answer Range Minimum Queries (RMQs) on the underlying array. This is particularly relevant in the encoding model, where the array is not accessible at query time, and a space lower bound of 2n-O(log n) bits is known. Given the numerous applications of RMQs, we use this problem as a case study for our experimental evaluation, testing our implementation on 11 real-world datasets. Our experiments show that, on almost every dataset, our implementation is the most space-efficient, using as few as 0.11n bits, while still delivering practical query times.
Cite as

Gabriel Carmona and Filippo Lari. Compressing Highly Repetitive Binary Trees with an Application to Range Minimum Queries. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{carmona_et_al:LIPIcs.SEA.2026.10,
  author =	{Carmona, Gabriel and Lari, Filippo},
  title =	{{Compressing Highly Repetitive Binary Trees with an Application to Range Minimum Queries}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.10},
  URN =		{urn:nbn:de:0030-drops-260140},
  doi =		{10.4230/LIPIcs.SEA.2026.10},
  annote =	{Keywords: tree compression, range minimum query, compact data structures, algorithm engineering, experimental evaluation}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.11
Wavelet Forests Revisited

Authors: Eric Chiu and Dominik Kempa

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
Rank and select queries are basic operations on sequences, with applications in compressed text indexes and other space-efficient data structures. One of the standard data structures supporting these queries is the wavelet tree. In this paper, we study wavelet forests, that is, wavelet-tree structures based on the fixed-block compression boosting technique. Such structures partition the input sequence into fixed-size blocks and build a separate wavelet tree for each block. Previous work showed that this approach yields strong practical performance for rank queries. We extend wavelet forests to support select queries. We show that select support can be added with little additional space overhead and that the resulting structures remain practically efficient. In experiments on a range of non-repetitive and repetitive inputs, wavelet forests are competitive with, and in most cases outperform, standalone wavelet-tree implementations. We also study the effect of internal parameters, including superblock size and navigational data, on select-query performance.
Cite as

Eric Chiu and Dominik Kempa. Wavelet Forests Revisited. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 11:1-11:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chiu_et_al:LIPIcs.SEA.2026.11,
  author =	{Chiu, Eric and Kempa, Dominik},
  title =	{{Wavelet Forests Revisited}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{11:1--11:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.11},
  URN =		{urn:nbn:de:0030-drops-260152},
  doi =		{10.4230/LIPIcs.SEA.2026.11},
  annote =	{Keywords: wavelet tree, wavelet forest, select queries}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.12
Fast Select Queries Using Hybrid Bitvectors

Authors: Eric Chiu and Dominik Kempa

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
One of the central problems in the design of compressed data structures is the efficient support for rank and select queries on bitvectors. These two operations form the backbone of more complex data structures used for the compact representation of texts, trees, graphs, or grids. One effective solution is the so-called hybrid bitvector implementation, which partitions the input bitvector into blocks and adaptively selects an encoding method - such as run-length, plain, or minority encoding - based on local redundancy. Experiments have shown that hybrid bitvectors achieve excellent all-around performance on repetitive and non-repetitive inputs. Current hybrid bitvector implementations, however, support only rank queries (i.e., counting the number of ones up to a given position) and lack support for select queries (which ask for the position of a given occurrence of a given bit), which limits their applicability. In this paper, we propose a method to add support for select queries to hybrid bitvectors, and we evaluate the resulting implementation on repetitive and non-repetitive inputs. Our results show that hybrid bitvectors offer very strong all-around performance, combining high query speed with space efficiency and remaining consistently on or near the Pareto frontier.
Cite as

Eric Chiu and Dominik Kempa. Fast Select Queries Using Hybrid Bitvectors. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 12:1-12:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chiu_et_al:LIPIcs.SEA.2026.12,
  author =	{Chiu, Eric and Kempa, Dominik},
  title =	{{Fast Select Queries Using Hybrid Bitvectors}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{12:1--12:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.12},
  URN =		{urn:nbn:de:0030-drops-260168},
  doi =		{10.4230/LIPIcs.SEA.2026.12},
  annote =	{Keywords: compressed bitvectors, hybrid bitvector, select queries}
}
Document
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.
Cite as

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.CPM.2026.36
Set Parameterized Matching via Multi-Layer Hashing

Authors: Moshe Lewenstein and Ely Porat

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

Abstract
We study the set parameterized matching problem, a generalization of the classical parameterized matching problem introduced by Baker [Baker, 1993; Baker, 1997]. In set parameterized matching, both the pattern and text are sequences where each position contains a set of characters rather than a single character. Two set-strings parameterized match if there exists a bijection between their alphabets that maps one to the other set-wise. Boussidan [Aaron Boussidan, 2025] introduced this problem for the case of equal-length set-strings. We present a randomized algorithm running in O(N + M) time with high probability, where N is the text size and M is the pattern size. Our approach employs a novel three-layer hashing scheme based on Karp-Rabin fingerprinting that addresses the challenges of (1) the size blowup in representations of the problem, (2) set-to-set matching, and (3) the dynamic nature of encodings of text substrings during pattern scanning.
Cite as

Moshe Lewenstein and Ely Porat. Set Parameterized Matching via Multi-Layer Hashing. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lewenstein_et_al:LIPIcs.CPM.2026.36,
  author =	{Lewenstein, Moshe and Porat, Ely},
  title =	{{Set Parameterized Matching via Multi-Layer Hashing}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{36:1--36:18},
  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.2026.36},
  URN =		{urn:nbn:de:0030-drops-259620},
  doi =		{10.4230/LIPIcs.CPM.2026.36},
  annote =	{Keywords: Set Parameterized Matching, Pattern Matching, Randomized Algorithms, Hashing, Parameterized Matching}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.35
Path-Reporting Distance Oracles for Vertex-Labeled Graphs

Authors: Ofer Neiman and Alon Spector

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
Let G = (V,E) be a weighted undirected graph, with n vertices. A distance oracle is a data structure that can quickly answer distance queries, with some stretch factor. A seminal work of [Thorup and Zwick, 2005], given an integer k ≥ 1, provides such an oracle with stretch 2k-1, query time O(k), and size O(k⋅ n^{1+1/k}). Furthermore, this oracle can also report a path in G corresponding to the returned distance. In this paper we focus on vertex-labeled graphs, in which each vertex is given a label from a set L of size 𝓁. A vertex-label distance oracle answers queries of the form (v,λ), where v ∈ V and λ ∈ L, by reporting (an approximation to) the distance from v to the closest vertex of label λ. Following [Danny Hermelin et al., 2011], it was shown in [Chechik, 2012] that for any integer k > 1, there exists a vertex-label distance oracle with stretch 4k-5, query time O(k), and size O(k⋅ n⋅ 𝓁^{1/k}). This state-of-the-art result suffers from two main drawbacks: The stretch is roughly a factor of 2 larger than in [Thorup and Zwick, 2005], and it is not path-reporting. We address these concerns in this work, and provide the following results. - First, we devise a path-reporting vertex-label distance oracle, at the cost of a slight increase in stretch and size. For any constant 0 < ε < 1, our oracle has stretch (4k-5)⋅(1+ε), query time O(k), and size O(n^{1+o(1)}⋅ 𝓁^{1/k}). - Second, we show how to improve the stretch to the optimal 2k-1, at the cost of mildly increasing the query time. Specifically, we devise a vertex-label distance oracle with stretch 2k-1, query time O(𝓁^{1/k}⋅log n), and size O(k⋅ n⋅ 𝓁^{1/k}).
Cite as

Ofer Neiman and Alon Spector. Path-Reporting Distance Oracles for Vertex-Labeled Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{neiman_et_al:LIPIcs.SWAT.2026.35,
  author =	{Neiman, Ofer and Spector, Alon},
  title =	{{Path-Reporting Distance Oracles for Vertex-Labeled Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{35:1--35:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.35},
  URN =		{urn:nbn:de:0030-drops-260719},
  doi =		{10.4230/LIPIcs.SWAT.2026.35},
  annote =	{Keywords: Graph Algorithms, Shortest Paths, Distance Oracles}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.2
Near-Real-Time Solutions for Online String Problems

Authors: Dominik Köppl and Gregory Kucherov

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

Abstract
Based on the Breslauer-Italiano online suffix tree construction algorithm (2013) with double logarithmic worst-case guarantees on the update time per letter, we develop near-real-time algorithms for several classical problems on strings, including the computation of the longest repeating suffix array, the (reversed) Lempel-Ziv 77 factorization, and the maintenance of minimal unique substrings, all in an online manner. Our solutions improve over the best known running times for these problems in terms of the worst-case time per letter, for which we achieve a poly-log-logarithmic time complexity, within a linear space. Best known results for these problems require a poly-logarithmic time complexity per letter or only provide amortized complexity bounds. As a result of independent interest, we give conversions between the longest previous factor array and the longest repeating suffix array in space and time bounds based on their irreducible representations, which can have sizes sublinear in the length of the input string.
Cite as

Dominik Köppl and Gregory Kucherov. Near-Real-Time Solutions for Online String Problems. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{koppl_et_al:LIPIcs.CPM.2026.2,
  author =	{K\"{o}ppl, Dominik and Kucherov, Gregory},
  title =	{{Near-Real-Time Solutions for Online String Problems}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{2:1--2:17},
  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.2026.2},
  URN =		{urn:nbn:de:0030-drops-259287},
  doi =		{10.4230/LIPIcs.CPM.2026.2},
  annote =	{Keywords: online algorithms, string algorithms, suffix tree, real-time computation, Lempel-Ziv factorization, minimal unique substrings}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.3
Computing k-mers in Graphs

Authors: Jarno N. Alanko and Máximo Pérez-López

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

Abstract
We initiate the study of computational problems on k-mers (strings of length k) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct k-mers found on the walks of a graph. We establish that this is #P-hard, even on connected deterministic DAGs. However, in the class of deterministic Wheeler graphs (Gagie, Manzini, and Sirén, TCS 2017), we show that distinct k-mers of such a graph W = (V, E) can be counted using O(|W|k) or O(n⁴ log k) arithmetic operations, where n = |V|, m = |E| and |W| = n+m. The latter result uses a new generalization of the technique of prefix doubling to Wheeler graphs. To generalize our results beyond Wheeler graphs, we discuss ways to transform a graph into a Wheeler graph in a manner that preserves the k-mers. As an application of our k-mer counting algorithms, we construct a representation of the de Bruijn graph of the k-mers that occupies O(n_k + |W|k log(max_{1 ≤ 𝓁 ≤ k} n_𝓁) + σlog m) bits of space, where n_𝓁 is the number of distinct 𝓁-mers in the Wheeler graph, and σ is the size of the alphabet. We show how to construct it in the same time complexity. Given that the Wheeler graph can be exponentially smaller than the de Bruijn graph, for large k this provides a theoretical improvement over previous de Bruijn graph construction methods from graphs, which must spend Ω(k) time per k-mer in the graph.
Cite as

Jarno N. Alanko and Máximo Pérez-López. Computing k-mers in Graphs. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 3:1-3:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alanko_et_al:LIPIcs.CPM.2026.3,
  author =	{Alanko, Jarno N. and P\'{e}rez-L\'{o}pez, M\'{a}ximo},
  title =	{{Computing k-mers in Graphs}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{3:1--3:17},
  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.2026.3},
  URN =		{urn:nbn:de:0030-drops-259294},
  doi =		{10.4230/LIPIcs.CPM.2026.3},
  annote =	{Keywords: Wheeler graph, Wheeler language, de Bruijn graph, graph, k-mer, q-gram, DFA, #P-hard}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.5
Efficient Grammar Compression via RLZ-Based RePair

Authors: Rahul Varki, Travis Gagie, and Christina Boucher

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

Abstract
Among grammar-based compression techniques, RePair is a notable offline encoding scheme known for its simplicity and powerful combinatorial properties, producing compact grammars by repeatedly replacing the most frequent adjacent pairs of symbols, known as bigrams. However, RePair’s memory usage scales poorly with input size, as it loads the entire text into memory. In contrast, Relative Lempel-Ziv (RLZ) parsing offers a scalable and lightweight online encoding scheme that losslessly represents a text in terms of phrases that refer to a reference string, but it often fails to expose deeper structural patterns. We introduce an algorithm that produces a RePair grammar from the RLZ parse of the input, leveraging the strengths of both methods. Our method, RLZ-RePair, performs bigram replacements systematically, preserving the integrity of the RLZ phrases throughout the RePair iterations. When the reference is well chosen, our method achieves the same grammar as standard RePair while significantly reducing both memory usage and the number of bigram replacements. In particular, we show that RLZ-RePair can reduce memory usage by more than 80% while incurring only a modest runtime increase compared to RePair. To our knowledge, RLZ-RePair is one of the first scalable methods that constructs exact RePair grammars, resulting in a grammar-based compressor that is both practical for large datasets and faithful to the theoretical elegance of RePair.
Cite as

Rahul Varki, Travis Gagie, and Christina Boucher. Efficient Grammar Compression via RLZ-Based RePair. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{varki_et_al:LIPIcs.CPM.2026.5,
  author =	{Varki, Rahul and Gagie, Travis and Boucher, Christina},
  title =	{{Efficient Grammar Compression via RLZ-Based RePair}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{5:1--5:15},
  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.2026.5},
  URN =		{urn:nbn:de:0030-drops-259310},
  doi =		{10.4230/LIPIcs.CPM.2026.5},
  annote =	{Keywords: RePair, RLZ, Grammar Compression}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.13
Faster Algorithms for Shortest Unique or Absent Substrings

Authors: Panagiotis Charalampopoulos, Manal Mohamed, Solon P. Pissis, Hilde Verbeek, and Wiktor Zuba

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We revisit two well-known algorithmic problems on strings: computing a shortest unique substring (SUS) and a shortest absent substring (SAS) in a string S of length n. Both problems admit folklore 𝒪(n)-time solutions using the suffix tree of S. However, for small alphabets, this complexity is not necessarily optimal in the word RAM model, where a string of length n over alphabet [0,σ) can be stored in 𝒪(n log σ/log n) space and read in 𝒪(n log σ/log n) time. We present an 𝒪(n log σ/√{log n})-time algorithm for computing a SUS in S. This algorithm decomposes the problem according to the length and the period of the sought substring and uses several tools and techniques, such as synchronizing sets, the analysis of runs, and wavelet trees, to reduce the computation of a SUS to a simple geometric problem. Further, we adapt this algorithm and combine it with an efficient construction of de Bruijn sequences in order to obtain an 𝒪(n log σ/√{log n})-time algorithm for computing a SAS in S.
Cite as

Panagiotis Charalampopoulos, Manal Mohamed, Solon P. Pissis, Hilde Verbeek, and Wiktor Zuba. Faster Algorithms for Shortest Unique or Absent Substrings. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charalampopoulos_et_al:LIPIcs.SWAT.2026.13,
  author =	{Charalampopoulos, Panagiotis and Mohamed, Manal and Pissis, Solon P. and Verbeek, Hilde and Zuba, Wiktor},
  title =	{{Faster Algorithms for Shortest Unique or Absent Substrings}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.13},
  URN =		{urn:nbn:de:0030-drops-260493},
  doi =		{10.4230/LIPIcs.SWAT.2026.13},
  annote =	{Keywords: string algorithms, unique substrings, absent substrings, absent words}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.26
The Communication Complexity of Pattern Matching with Edits Revisited

Authors: Tomasz Kociumaka, Jakob Nogler, and Philip Wellnitz

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

Abstract
The decades-old Pattern Matching with Edits problem, given a length-n string T (the text), a length-m string P (the pattern), and a positive integer k (the threshold), asks to list the k-error occurrences of P in T, that is, all fragments of T whose edit distance to P is at most k. The one-way communication complexity of this problem is the minimum number of bits that Alice, given an instance (P,T,k) of the problem, must send to Bob so that Bob can reconstruct the answer solely from that message. In recent work [STOC'24], we showed that, in the natural parameter regime 0 < k < m < n/2, Ω(n/m ⋅ k log(m/k)) bits are necessary and 𝒪(n/m ⋅ k log² m) bits are sufficient for this problem. More generally, for strings over an alphabet Σ, we gave an 𝒪(n/m ⋅ k log m log(m|Σ|))-bit encoding that allows one to recover a shortest sequence of edits for every k-error occurrence of P in T. In this paper, we revisit the original proof and improve the encoding size to 𝒪(n/m ⋅ k log (m|Σ|/k)), which matches the lower bound for constant-sized alphabets. We further establish a new tight lower bound of Ω(n/m ⋅ k log(m|Σ|/k)) for the edit sequence reporting variant we solve. Our encoding size also matches the communication complexity established for the simpler Pattern Matching with Mismatches problem in the context of streaming algorithms [Clifford, Kociumaka, Porat; SODA'19].
Cite as

Tomasz Kociumaka, Jakob Nogler, and Philip Wellnitz. The Communication Complexity of Pattern Matching with Edits Revisited. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kociumaka_et_al:LIPIcs.CPM.2026.26,
  author =	{Kociumaka, Tomasz and Nogler, Jakob and Wellnitz, Philip},
  title =	{{The Communication Complexity of Pattern Matching with Edits Revisited}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{26:1--26:15},
  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.2026.26},
  URN =		{urn:nbn:de:0030-drops-259525},
  doi =		{10.4230/LIPIcs.CPM.2026.26},
  annote =	{Keywords: Edit distance, Pattern matching, Communication complexity}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.29
The TAG Array of a Multiple Sequence Alignment

Authors: Jannik Olbrich and Enno Ohlebusch

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

Abstract
Modern genomic analyses increasingly rely on pangenomes, that is, representations of the genome of entire populations. The simplest representation of a pangenome is a set of individual genome sequences. Compared to e.g. sequence graphs, this has the advantage that efficient exact search via indexes based on the Burrows-Wheeler Transform (BWT) is possible, that no chimeric sequences are created, and that the results are not influenced by heuristics. However, such an index may report a match in thousands of positions even if these all correspond to the same locus, making downstream analysis unnecessarily more expensive. For sufficiently similar sequences (e.g. human chromosomes), a multiple sequence alignment (MSA) can be computed. Since an MSA tends to group similar strings in the same columns, it is likely that a string occurring thousands of times in the pangenome can be described by very few columns in the MSA. We describe a method to tag entries in the BWT with the corresponding column in the MSA and develop an index that can map matches in the BWT to columns in the MSA in time proportional to the output. As a by-product, we can project a match to a designated reference genome, a capability that current pangenome aligners lack.
Cite as

Jannik Olbrich and Enno Ohlebusch. The TAG Array of a Multiple Sequence Alignment. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{olbrich_et_al:LIPIcs.CPM.2026.29,
  author =	{Olbrich, Jannik and Ohlebusch, Enno},
  title =	{{The TAG Array of a Multiple Sequence Alignment}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{29:1--29:14},
  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.2026.29},
  URN =		{urn:nbn:de:0030-drops-259555},
  doi =		{10.4230/LIPIcs.CPM.2026.29},
  annote =	{Keywords: Burrows-Wheeler Transform, pattern matching, index data structure, pangenomics}
}
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