88 Search Results for "Boucher, Christina"

Volume

LIPIcs, Volume 242

22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)

WABI 2022, September 5-7, 2022, Potsdam, Germany

Editors: Christina Boucher and Sven Rahmann

Document
DOI: 10.4230/LIPIcs.SEA.2026.4
Integer Programming Models for the Median of a 0-1 String Set Under Levenshtein Distance

Authors: Claudio Arbib, Andrea D'Ascenzo, Oya E. Karaşan, and Andrea Pizzuti

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

Abstract
The Median String Problem calls for finding a string that minimizes the average distance from a given set of strings. Under the Levenshtein (or edit) metric, the problem is NP-hard even for binary strings. We devised two novel integer linear programming models for this case and tested them against the only formulation we are aware of in the literature. Our numerical experiments attest to the efficacy of the proposed approach.
Cite as

Claudio Arbib, Andrea D'Ascenzo, Oya E. Karaşan, and Andrea Pizzuti. Integer Programming Models for the Median of a 0-1 String Set Under Levenshtein Distance. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{arbib_et_al:LIPIcs.SEA.2026.4,
  author =	{Arbib, Claudio and D'Ascenzo, Andrea and Kara\c{s}an, Oya E. and Pizzuti, Andrea},
  title =	{{Integer Programming Models for the Median of a 0-1 String Set Under Levenshtein Distance}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{4:1--4:15},
  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.2026.4},
  URN =		{urn:nbn:de:0030-drops-260081},
  doi =		{10.4230/LIPIcs.SEA.2026.4},
  annote =	{Keywords: Levenshtein Distance, Median String Problem, Integer Programming}
}
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.
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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.2026.9
Bounding the Average Move Structure Query for Faster and Smaller RLBWT Permutations

Authors: Nathaniel K. Brown and Ben Langmead

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

Abstract
The move structure represents permutations with long contiguously permuted intervals in compressed space with optimal query time. They have become an important feature of compressed text indexes using space proportional to the number of Burrows-Wheeler Transform (BWT) runs, often applied in genomics. This is in thanks not only to theoretical improvements over past approaches, but great cache efficiency and average case query time in practice. This is true even without using the worst case guarantees provided by the interval splitting balancing of the original result. In this paper, we show that an even simpler type of splitting, length capping by truncating long intervals, bounds the average move structure query time to optimal whilst obtaining a superior construction time than the traditional approach. This also proves constant query time when amortized over a full traversal of a single cycle permutation from an arbitrary starting position. Such a scheme has surprising benefits both in theory and practice. For a move structure with r runs over a domain n, we replace all O(r log n)-bit components to reduce the overall representation by O(r log r)-bits. The worst case query time is also improved to O(log n/r) without balancing. An O(r)-time and space construction lets us apply the method to run-length encoded BWT (RLBWT) permutations such as LF and ϕ to obtain optimal-time algorithms for BWT inversion and suffix array (SA) enumeration in O(r) working space. Finally, we introduce the Orbit library, providing flexible plug and play move structure support, and use it to evaluate our splitting approach. Experiments find length capping construction is faster and uses less memory than balancing, and results in faster move structure queries: up to ∼ 17 times faster when compared to an unbalanced representation of ϕ. We also see a space reduction in practice, with at least a ∼ 40% disk size decrease for LF across large repetitive genomic collections when compared to a balanced/unbalanced move structure.
Cite as

Nathaniel K. Brown and Ben Langmead. Bounding the Average Move Structure Query for Faster and Smaller RLBWT Permutations. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{brown_et_al:LIPIcs.SEA.2026.9,
  author =	{Brown, Nathaniel K. and Langmead, Ben},
  title =	{{Bounding the Average Move Structure Query for Faster and Smaller RLBWT Permutations}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{9:1--9:15},
  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.2026.9},
  URN =		{urn:nbn:de:0030-drops-260136},
  doi =		{10.4230/LIPIcs.SEA.2026.9},
  annote =	{Keywords: Move Structure, Burrows-Wheeler Transform, Permutation}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.19
Breaking 2-Cores for Invertible Bloom Lookup Tables by Structure Prediction

Authors: Vojtěch Gaďurek and Pavel Veselý

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

Abstract
Invertible Bloom Lookup Tables (IBLTs) provide a highly space-efficient way to reconstruct small sets resulting from a large number of insertions and deletions of elements, such as in streaming or distributed computation of the symmetric difference of similar sets. The set recovery process succeeds if the IBLT size is at least 1.22 times the size of the encoded set; otherwise, a 2-core occurs with high probability in the corresponding random hypergraph. However, the sets in practice often exhibit structure that allows for performance beyond worst-case bounds. Here, we demonstrate that structured sets - such as the k-mers in the symmetric difference of two closely related genomes - can be recovered with an IBLT of significantly smaller size. We achieve this by employing structure-aware predictors to break the 2-core whenever the recovery process gets stuck. Importantly, this approach modifies only the decoding procedure, leaving the IBLT data structure unchanged. We prove that even a weak matching-based predictor enables the recovery of 27% more elements than the nominal IBLT size. Equipped with simple predictors for k-mers of genomic datasets, we demonstrate that recovering a symmetric difference with high probability can be done with an IBLT of size only 66% of the encoded set size for k = 31, improving the space efficiency by almost a factor of two. Moreover, we design an improved method for k-mers with large k that combines subsampling with nearly perfect prediction via fingerprinting and achieves a scaling property, requiring only O(M log M) bits for recovering M k-mers, instead of Θ(k⋅M) bits of the standard IBLT. Overall, our results highlight the possibility of significant space-efficiency improvements for IBLTs on datasets with predictable structure.
Cite as

Vojtěch Gaďurek and Pavel Veselý. Breaking 2-Cores for Invertible Bloom Lookup Tables by Structure Prediction. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gadurek_et_al:LIPIcs.SEA.2026.19,
  author =	{Ga\v{d}urek, Vojt\v{e}ch and Vesel\'{y}, Pavel},
  title =	{{Breaking 2-Cores for Invertible Bloom Lookup Tables by Structure Prediction}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{19:1--19:24},
  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.2026.19},
  URN =		{urn:nbn:de:0030-drops-260237},
  doi =		{10.4230/LIPIcs.SEA.2026.19},
  annote =	{Keywords: Invertible Bloom Lookup Table, symmetric difference, k-mer sets}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.16
Efficient Large-Scale Text Precompression via Approximate LZ77 Parsings

Authors: Patrick Dinklage

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

Abstract
The LZ77 [Lempel and Ziv, 1977] compression scheme is ubiquitous: it lies at the core of everyday general-purpose standard compressors such as gzip or zstd, but also behind the scenes of many applications such as the compression of payloads transmitted in networks. Computing the exact LZ77 parsing is largely solved in theory: it can be done in sublinear time and space, in compressed space and in external memory, to name but some scenarios. However, these approaches are often impractical for everyday use due to their intensive time or space requirements. Standard compressors tackle this issue by introducing heuristics that go hand in hand with sophisticated encoding schemes to achieve very good compression fast and in small space, however, they only have a local view (e.g., a sliding window) on the input, potentially missing out on long-range repetitions that may be located far apart from one another. In this work, we design and implement - in C++ and leveraging shared-memory parallelism - compression pipelines that first precompress the input using an approximate LZ77 parsing taking care of long-range repetitions. This then serves as an assist to standard compressors for producing a succinct encoding of the remaining short and local repetitions. Similar approaches have been considered by [Kosolobov et al., 2020] and [Nalbach, 2024], respectively using Relative Lempel Ziv [Kuruppu et al. 2010] or the string synchronizing set [Kempa & Kociumaka, 2019]. We fill a gap taking the route via the prefix-free parsing [Boucher et al., 2019], using an intermediate result of [Hong et al., 2023]. On large repetitive inputs of tens of gigabytes, our pipelines are orders of magnitudes faster than the state of the art for computing the exact LZ77 parsing, use space less than the input size and still - despite producing more phrases - achieve the best overall compression in comparison to related work.
Cite as

Patrick Dinklage. Efficient Large-Scale Text Precompression via Approximate LZ77 Parsings. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dinklage:LIPIcs.SEA.2026.16,
  author =	{Dinklage, Patrick},
  title =	{{Efficient Large-Scale Text Precompression via Approximate LZ77 Parsings}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{16:1--16:20},
  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.2026.16},
  URN =		{urn:nbn:de:0030-drops-260204},
  doi =		{10.4230/LIPIcs.SEA.2026.16},
  annote =	{Keywords: compression, algorithm engineering, parallel computation}
}
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.CPM.2026.7
Optimal Structure for Prefix-Substring Queries

Authors: Paweł Gawrychowski, Florin Manea, and Jonas Richardsen

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

Abstract
The prefix-substring matching problem [Gu, Farach, and Beigel, SODA 1994] consists in preprocessing a string s of length n for the following queries: given a triple (i, j, k) ∈ {0, … , |s|}³ with 1 ≤ j ≤ k, representing a prefix s[1:i] and a substring s[j:k] of s, find the longest prefix of s that is a suffix of s[1:i]s[j:k]. This is an useful primitive in e.g. dynamic text indexing, compressed pattern matching, and pattern matching on block graphs. The border tree uses some basic periodicity properties to answer such queries in 𝒪(log n) time after 𝒪(n) time preprocessing of s. We design a linear-space structure that answers such queries in constant time after 𝒪(n) time preprocessing of s over a polynomial alphabet, which is worst-case optimal.
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Paweł Gawrychowski, Florin Manea, and Jonas Richardsen. Optimal Structure for Prefix-Substring Queries. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2026.7,
  author =	{Gawrychowski, Pawe{\l} and Manea, Florin and Richardsen, Jonas},
  title =	{{Optimal Structure for Prefix-Substring Queries}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{7:1--7:20},
  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.2026.7},
  URN =		{urn:nbn:de:0030-drops-259333},
  doi =		{10.4230/LIPIcs.CPM.2026.7},
  annote =	{Keywords: Border Tree, Prefix-Substring Query, Data Structures}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.16
Merging RLBWTs Adaptively

Authors: Travis Gagie

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

Abstract
We show how to merge two run-length compressed Burrows-Wheeler Transforms (RLBWTs) into a run-length compressed extended Burrows-Wheeler Transform (eBWT) in O (r) space and O ((r + L) log (m + n)) time, where m and n are the lengths of the uncompressed strings, r is the number of runs in the final eBWT and L is the sum of its irreducible LCP values.
Cite as

Travis Gagie. Merging RLBWTs Adaptively. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gagie:LIPIcs.CPM.2026.16,
  author =	{Gagie, Travis},
  title =	{{Merging RLBWTs Adaptively}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{16:1--16:15},
  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.2026.16},
  URN =		{urn:nbn:de:0030-drops-259420},
  doi =		{10.4230/LIPIcs.CPM.2026.16},
  annote =	{Keywords: Burrows-Wheeler Transform, run-length compression, RLBWT, construction, merging}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.23
Improved Bounds on the Sum of Exponents of Runs in a String

Authors: Arkadiusz Czarkowski

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

Abstract
A substring of a word is a run if it is at least twice as long as its minimum period and cannot be extended to either side with the same period. The exponent of a run is the quotient of its length and its minimum period. ρ(n) is the maximum number of runs in a string of length n, while σ(n) is the maximum sum of exponents of runs in a string of length n. While quite tight bounds on ρ(n) are known (0.944575712n ≤ ρ(n) ≤ n), the best upper bound on σ(n) is 3n whereas the best lower bound on σ(n) is 2.035n. In this paper, we improve the upper bound on σ(n) to 2.3n and the lower bound on σ(n) to 2.04448n. We also provide an improved upper bound on σ(n) of 2.2n in the case of a binary alphabet. Our results are achieved using a combination of theoretical and computer-based approaches.
Cite as

Arkadiusz Czarkowski. Improved Bounds on the Sum of Exponents of Runs in a String. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{czarkowski:LIPIcs.CPM.2026.23,
  author =	{Czarkowski, Arkadiusz},
  title =	{{Improved Bounds on the Sum of Exponents of Runs in a String}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{23:1--23:18},
  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.2026.23},
  URN =		{urn:nbn:de:0030-drops-259494},
  doi =		{10.4230/LIPIcs.CPM.2026.23},
  annote =	{Keywords: strings, runs, sum of exponents of runs, Lyndon words, L-roots, maximal repetitions, combinatorics on words}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.22
Optimal-Time Mapping in Run-Length Compressed PBWT

Authors: Paola Bonizzoni, Davide Cozzi, and Younan Gao

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

Abstract
The Positional Burrows-Wheeler Transform (PBWT) is a data structure designed for efficiently representing and querying large collections of sequences, such as haplotype panels in genomics. Forward and backward stepping operations - analogues to LF- and FL-mapping in the traditional BWT - are fundamental to the PBWT, underpinning many algorithms based on the PBWT for haplotype matching and related analyses. Although the run-length encoded variant of the PBWT (also known as the μ-PBWT) achieves O(r̃)-word space usage, where r̃ is the total number of runs, no data structure supporting both forward and backward stepping in constant time within this space bound was previously known. In this paper, we consider the multi-allelic PBWT that is extended from its original binary form to a general ordered alphabet {0, … , σ-1}. We first establish bounds on the size r̃ and then introduce a new O(r̃)-word data structure built over a list of haplotypes {S_1, … , S_h}, each of length w, that supports constant-time forward and backward stepping. We further revisit two key applications - haplotype retrieval and prefix search - leveraging our efficient forward stepping technique. Specifically, we design an O(r̃)-word space data structure that supports haplotype retrieval in O(log log_w h + w) time. For prefix search, we present an O(h + r̃)-word data structure that answers queries in O(m' log log_w σ + occ) time, where m' denotes the length of the longest common prefix returned and occ denotes the number of haplotypes prefixed the longest prefix.
Cite as

Paola Bonizzoni, Davide Cozzi, and Younan Gao. Optimal-Time Mapping in Run-Length Compressed PBWT. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bonizzoni_et_al:LIPIcs.CPM.2026.22,
  author =	{Bonizzoni, Paola and Cozzi, Davide and Gao, Younan},
  title =	{{Optimal-Time Mapping in Run-Length Compressed PBWT}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{22:1--22:18},
  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.2026.22},
  URN =		{urn:nbn:de:0030-drops-259487},
  doi =		{10.4230/LIPIcs.CPM.2026.22},
  annote =	{Keywords: PBWT, LF-Mapping, prefix searches, run-length encoding}
}
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}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.33
The Smallest String Attractors of Fibonacci and Period-Doubling Words

Authors: Mutsunori Banbara, Hideo Bannai, Peaker Guo, Dominik Köppl, Takuya Mieno, and Yoshio Okamoto

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

Abstract
A string attractor of a string T[1..|T|] is a set of positions Γ of T such that any substring w of T has an occurrence that crosses a position in Γ, i.e., there is a position i such that w = T[i..i+|w|-1] and the intersection [i,i+|w|-1]∩ Γ is nonempty. The size of the smallest string attractor of Fibonacci words is known to be 2. We completely characterize the set of all smallest string attractors of Fibonacci words, and show a recursive formula describing the 2^{n-4} + 2^{⌈n/2⌉ - 2} distinct position pairs that are the smallest string attractors of the nth Fibonacci word for n ≥ 7. Similarly, the size of the smallest string attractor of period-doubling words is known to be 2. We also completely characterize the set of all smallest string attractors of period-doubling words, and show a formula describing the two distinct position pairs that are the smallest string attractors of the nth period-doubling word for n ≥ 2. Our results show that strings with the same smallest attractor size can have a drastically different number of distinct smallest attractors.
Cite as

Mutsunori Banbara, Hideo Bannai, Peaker Guo, Dominik Köppl, Takuya Mieno, and Yoshio Okamoto. The Smallest String Attractors of Fibonacci and Period-Doubling Words. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{banbara_et_al:LIPIcs.CPM.2026.33,
  author =	{Banbara, Mutsunori and Bannai, Hideo and Guo, Peaker and K\"{o}ppl, Dominik and Mieno, Takuya and Okamoto, Yoshio},
  title =	{{The Smallest String Attractors of Fibonacci and Period-Doubling Words}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{33:1--33:21},
  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.2026.33},
  URN =		{urn:nbn:de:0030-drops-259599},
  doi =		{10.4230/LIPIcs.CPM.2026.33},
  annote =	{Keywords: String attractors, Fibonacci words, Period-doubling words, Combinatorics on words}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.30
Constructing Suffixient Arrays Revisited

Authors: Paola Bonizzoni, Younan Gao, and Brian Riccardi

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

Abstract
Recently, Cenzato et al. proposed a new text index, called the suffixient array, which is a subset of the suffix array and supports locating a single pattern occurrence or finding its maximal exact matches (MEMs), assuming random access to the input text T[1..n] is available. They show that, given the suffix array, the longest common prefix array, and the Burrows-Wheeler transform (BWT) of the reverse of T[1..n] over an alphabet {1,…,σ}, a suffixient array can be constructed in linear time. However, their construction algorithms require multiple scans of these arrays. When restricted to a single pass over the arrays, they present an alternative construction algorithm running in O(n + r log σ) time, where r is the number of runs in the BWT of the reversed text. In this paper, we present a new one-pass algorithm that constructs a suffixient array in linear time under the standard RAM model.
Cite as

Paola Bonizzoni, Younan Gao, and Brian Riccardi. Constructing Suffixient Arrays Revisited. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bonizzoni_et_al:LIPIcs.CPM.2026.30,
  author =	{Bonizzoni, Paola and Gao, Younan and Riccardi, Brian},
  title =	{{Constructing Suffixient Arrays Revisited}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{30:1--30:18},
  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.2026.30},
  URN =		{urn:nbn:de:0030-drops-259564},
  doi =		{10.4230/LIPIcs.CPM.2026.30},
  annote =	{Keywords: Suffixient set, suffixient array, right-maximal substring, linear-time algorithm}
}
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