11 Search Results for "Grabowski, Adam"

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.2026.20
QuadRank: Engineering a High Throughput Rank

Authors: Ragnar Groot Koerkamp

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

Abstract
Motivation. Given a text, a query rank(q, c) counts the number of occurrences of character c among the first q characters of the text. Space-efficient methods to answer these rank queries form an important building block in many succinct data structures. For example, the FM-index [Ferragina and Manzini, 2000] is a widely used data structure that uses rank queries to locate all occurrences of a pattern in a text. In bioinformatics applications, the goal is usually to process large inputs as fast as possible. Thus, data structures should have high throughput when used with many threads. Contributions. We first survey existing results on rank data structures. For the σ = 2 binary alphabet, we then develop BiRank, which has 3.28% space overhead. BiRank merges the central ideas of two recent papers: (1) we interleave (inline) offsets in each cache line of the underlying bit vector [Laws et al., 2024], reducing cache misses, and (2) these offsets are to the middle of each block so that only half of each needs popcounting [Gottlieb and Reinert, 2025]. In QuadRank (14.4% overhead), we extend these techniques to the σ = 4 (DNA) alphabet. Both data structures typically require only a single cache miss per query, making them highly suitable for high-throughput and memory-bound settings. To enable efficient batch-processing, we support prefetching the cache lines required to answer upcoming queries. Results. BiRank and QuadRank are around 1.5× and 2× faster than similar-overhead methods that do not use interleaving. Prefetching gives an additional 2× speedup, at which point the dual-channel DDR4 RAM bandwidth becomes a hard limit on the total throughput. With prefetching, both methods outperform all other methods apart from SPIDER [Laws et al., 2024] by 2×. When using QuadRank with prefetching in a toy count-only FM-index, QuadFm, this results in a smaller size and up to 4× speedup over Genedex, a state-of-the-art batching FM-index implementation. Conclusion. Optimizing data structures for high throughput, by minimizing cache misses and branch-misses and adding support for prefetching, can result in significant speedups when benchmarks are adjusted accordingly.
Cite as

Ragnar Groot Koerkamp. QuadRank: Engineering a High Throughput Rank. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{grootkoerkamp:LIPIcs.SEA.2026.20,
  author =	{Groot Koerkamp, Ragnar},
  title =	{{QuadRank: Engineering a High Throughput Rank}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{20:1--20:23},
  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.2026.20},
  URN =		{urn:nbn:de:0030-drops-260248},
  doi =		{10.4230/LIPIcs.SEA.2026.20},
  annote =	{Keywords: Rank, Succinct Data Structures, Cache Performance, Prefetching}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.14
Hardness Results on Characteristics for Elastic-Degenerate Strings

Authors: Dominik Köppl and Jannik Olbrich

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

Abstract
Generalizations of plain strings have been proposed as a compact way to represent a collection of nearly identical sequences or to express uncertainty at specific text positions by enumerating all possibilities. While a plain string stores a character at each of its positions, generalizations consider a set of characters (indeterminate strings), a set of strings of equal length (generalized degenerate strings, or shortly GD strings), or a set of strings of arbitrary lengths (elastic-degenerate strings, or shortly ED strings). These generalizations are of importance to compactly represent such type of data, and find applications in bioinformatics for representing and maintaining a set of genetic sequences of the same taxonomy or a multiple sequence alignment. To be of use, attention has been drawn to answering various query types such as pattern matching or measuring similarity of ED strings by generalizing techniques known to plain strings. However, for some types of queries, it has been shown that a generalization of a polynomial-time solvable query on classic strings becomes NP-hard on ED strings, e.g. [Russo et al., 2022]. In that light, we wonder about other types of queries that are of particular interest to bioinformatics: unique substrings, absent words, anti-powers, longest previous factors, and Lempel-Ziv-like compression schemes. While we obtain a polynomial time algorithm for a variation of longest previous factors, we show that all other problems are NP-hard to compute, some of them even under the restriction that the input can be modeled as an indeterminate or GD string.
Cite as

Dominik Köppl and Jannik Olbrich. Hardness Results on Characteristics for Elastic-Degenerate Strings. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 14:1-14:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{koppl_et_al:LIPIcs.CPM.2026.14,
  author =	{K\"{o}ppl, Dominik and Olbrich, Jannik},
  title =	{{Hardness Results on Characteristics for Elastic-Degenerate Strings}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{14:1--14:25},
  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.2026.14},
  URN =		{urn:nbn:de:0030-drops-259409},
  doi =		{10.4230/LIPIcs.CPM.2026.14},
  annote =	{Keywords: Elastic-degenerate strings, NP-hardness, longest common factor, minimal unique substring, minimal absent word, anti-power, longest previous factor}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.27
Exploring the Gap Between LCS and LCStr

Authors: Shay Golan, Matan Kraus, Ely Porat, and B. Riva Shalom

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

Abstract
The Longest Common Subsequence (LCS) problem and the Longest Common Substring (LCStr) problem are classical string problems with broad theoretical and practical significance. The former has a quadratic conditional lower bound [FOCS, 2015], while the latter admits a linear-time solution. In this paper, we study a natural variation of these problems, the Longest Common Subsequence-Substring (LCSS) problem. The LCSS problem seeks the longest string that is simultaneously a subsequence of one input string and a substring of the other. This variant bridges LCS and LCStr, raising intriguing algorithmic questions: Does the complexity of computing LCSS interpolate between the linear time of LCStr and the quadratic time of LCS? What about approximability? We also examine a natural extension of LCSS to multiple strings, parameterizing the balance between subsequence and substring requirements. Our results reveal several insights. First, under the SETH conjecture, the inherent complexity of LCSS is quadratic, similar to LCS. In contrast, we provide a linear-time approximation for LCSS. Finally, for the multi-string variant, unlike both problems, we design a quadratic-time algorithm, uncovering deeper structural properties of the problem. By studying the complexity of the LCSS problem, we aim to gain some understanding of what influences whether a variant of the LCS problem behaves more like the standard LCS or like LCStr. Our findings suggest that hybrid constraints can create computational "sweet spots," where problems become more tractable than their pure counterparts. This opens a broader research direction in constraint-mediated algorithm design. Beyond LCSS itself, our work highlights unexpected connections between subsequence and substring constraints, advancing the theoretical understanding of string problems and laying the foundation for new algorithmic techniques and complexity-theoretic insights in the rich space between classical string comparison paradigms.
Cite as

Shay Golan, Matan Kraus, Ely Porat, and B. Riva Shalom. Exploring the Gap Between LCS and LCStr. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{golan_et_al:LIPIcs.CPM.2026.27,
  author =	{Golan, Shay and Kraus, Matan and Porat, Ely and Shalom, B. Riva},
  title =	{{Exploring the Gap Between LCS and LCStr}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{27:1--27:21},
  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.2026.27},
  URN =		{urn:nbn:de:0030-drops-259535},
  doi =		{10.4230/LIPIcs.CPM.2026.27},
  annote =	{Keywords: Longest Common Subsequence, Longest Common Substring, Conditional Lower Bound}
}
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.
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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/OASIcs.SpaceCHI.2025.26
Movement in Low Gravity (MoLo) – LUNA: Biomechanical Modelling to Mitigate Lunar Surface Operation Risks

Authors: David Andrew Green

Published in: OASIcs, Volume 130, Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)

Abstract
The Artemis programme seeks to develop and test concepts, hardware and approaches to support long term habitation of the Lunar surface, and future missions to Mars. In preparation for the Artemis missions determination of tasks to be performed, the functional requirements of such tasks and as mission duration extends whether physiological deconditioning becomes functionally significant, compromising the crew member’s ability to perform critical tasks on the surface, and/or upon return to earth [MoLo-LUNA – leveraging the Molo programme (and several other activities) - could become a key supporting activity for LUNA incl. validation of the Puppeteer offloading system itself via creation of a complementary MoLo-LUNA-LAB. Furthermore, the MoLo-LUNA programme could become a key facilitator of simulator suit instrumentation/definition, broader astronaut training activities and mission architecture development – including Artemis mission simulations. By employing a Puppeteer system external to the LUNA chamber hall it will optimise utilisation and cost-effectiveness of LUNA, and as such represents a critical service to future LUNA stakeholders. Furthermore, MoLo-LUNA would generate a unique data set that can be leveraged to predict de-conditioning on the Lunar surface - and thereby optimise functionality, and minimise mission risk – including informing the need for, and prescription of exercise countermeasures on the Lunar Surface and in transit. Thus, MoLo-LUNA offers a unique opportunity to place LUNA, and ESA as a key ongoing provider of evidence to define, optimise and support crew Artemis surface missions.
Cite as

David Andrew Green. Movement in Low Gravity (MoLo) – LUNA: Biomechanical Modelling to Mitigate Lunar Surface Operation Risks. In Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025). Open Access Series in Informatics (OASIcs), Volume 130, pp. 26:1-26:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{green:OASIcs.SpaceCHI.2025.26,
  author =	{Green, David Andrew},
  title =	{{Movement in Low Gravity (MoLo) – LUNA: Biomechanical Modelling to Mitigate Lunar Surface Operation Risks}},
  booktitle =	{Advancing Human-Computer Interaction for Space Exploration (SpaceCHI 2025)},
  pages =	{26:1--26:11},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-384-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{130},
  editor =	{Bensch, Leonie and Nilsson, Tommy and Nisser, Martin and Pataranutaporn, Pat and Schmidt, Albrecht and Sumini, Valentina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SpaceCHI.2025.26},
  URN =		{urn:nbn:de:0030-drops-240166},
  doi =		{10.4230/OASIcs.SpaceCHI.2025.26},
  annote =	{Keywords: Locomotion, hypogravity, modelling, Lunar}
}
Document
DOI: 10.4230/OASIcs.Manzini.3
BWT for String Collections

Authors: Davide Cenzato, Zsuzsanna Lipták, Nadia Pisanti, Giovanna Rosone, and Marinella Sciortino

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract
We survey the different methods used for extending the BWT to collections of strings, following largely [Cenzato and Lipták, CPM 2022, Bioinformatics 2024]. We analyze the specific aspects and combinatorial properties of the resulting BWT variants and give a categorization of publicly available tools for computing the BWT of string collections. We show how the specific method used impacts on the resulting transform, including the number of runs, and on the dynamicity of the transform with respect to adding or removing strings from the collection. We then focus on the number of runs of these BWT variants and present the optimal BWT introduced in [Cenzato et al., DCC 2023], which implements an algorithm originally proposed by [Bentley et al., ESA 2020] to minimize the number of BWT-runs. We also discuss several recent heuristics and study their impact on the compression of biological sequences. We conclude with an overview of the applications and the impact of the BWT of string collections in bioinformatics.
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Davide Cenzato, Zsuzsanna Lipták, Nadia Pisanti, Giovanna Rosone, and Marinella Sciortino. BWT for String Collections. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 3:1-3:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cenzato_et_al:OASIcs.Manzini.3,
  author =	{Cenzato, Davide and Lipt\'{a}k, Zsuzsanna and Pisanti, Nadia and Rosone, Giovanna and Sciortino, Marinella},
  title =	{{BWT for String Collections}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{3:1--3:29},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.3},
  URN =		{urn:nbn:de:0030-drops-239113},
  doi =		{10.4230/OASIcs.Manzini.3},
  annote =	{Keywords: Burrows-Wheeler transform, Extended Burrows-Wheeler transform, compressed text indexes, text compression, string collections, bioinformatics}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.20
SimdMinimizers: Computing Random Minimizers, fast

Authors: Ragnar Groot Koerkamp and Igor Martayan

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

Abstract
Motivation. Because of the rapidly-growing amount of sequencing data, computing sketches of large textual datasets has become an essential preprocessing task. These sketches are typically much smaller than the input sequences, but preserve sufficient information for downstream analysis. Minimizers are an especially popular sketching technique and used in a wide variety of applications. They sample at least one out of every w consecutive k-mers. As DNA sequencers are getting more accurate, some applications can afford to use a larger w and hence sparser and smaller sketches. And as sketches get smaller, their analysis becomes faster, so the time spent sketching the full-sized input becomes more of a bottleneck. Methods. Our library simd-minimizers implements a random minimizer algorithm using SIMD instructions. It supports both AVX2 and NEON architectures. Its main novelty is two-fold. First, it splits the input into 8 chunks that are streamed over in parallel through all steps of the algorithm. This is enabled by using the completely deterministic two-stacks sliding window minimum algorithm, which seems not to have been used before for finding minimizers. Results. Our library is up to 6.8× faster than a scalar implementation of the rescan method when w = 5 is small, and 3.4× faster for larger w = 19. Computing canonical minimizers is less than 50% slower than computing forward minimizers, and over 15× faster than the existing implementation in the minimizer-iter crate. Our library finds all (canonical) minimizers of a 3.2 Gbp human genome in 5.2 (resp. 6.7) seconds.
Cite as

Ragnar Groot Koerkamp and Igor Martayan. SimdMinimizers: Computing Random Minimizers, fast. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grootkoerkamp_et_al:LIPIcs.SEA.2025.20,
  author =	{Groot Koerkamp, Ragnar and Martayan, Igor},
  title =	{{SimdMinimizers: Computing Random Minimizers, fast}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{20:1--20:19},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-232581},
  doi =		{10.4230/LIPIcs.SEA.2025.20},
  annote =	{Keywords: Minimizers, Randomized algorithms, Sketching, Hashing}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.28
Faster Approximate Elastic-Degenerate String Matching - Part A

Authors: Solon P. Pissis, Jakub Radoszewski, and Wiktor Zuba

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
An elastic-degenerate (ED) string 𝐓 is a sequence 𝐓 = 𝐓[1] ⋯ 𝐓[n] of n finite sets of strings. The cardinality m of 𝐓 is the total number of strings in 𝐓[i], for all i ∈ [1..n]. The size N of 𝐓 is the total length of all m strings of 𝐓. ED strings have been introduced to represent a set of closely-related DNA sequences. Let P = P[1..p] be a pattern of length p and k > 0 be an integer. We consider the problem of k-Approximate ED String Matching (EDSM): searching k-approximate occurrences of P in the language of 𝐓. We call k-Approximate EDSM under the Hamming distance, k-Mismatch EDSM; and we call k-Approximate EDSM under edit distance, k-Edit EDSM. Bernardini et al. (Theoretical Computer Science, 2020) showed a simple 𝒪(k m p + kN)-time algorithm for k-Mismatch EDSM and an 𝒪(k² m p + kN)-time algorithm for k-Edit EDSM. We improve the dependency on k in both results, obtaining an Õ(k^{2/3}mp+√kN)-time algorithm for k-Mismatch EDSM and an Õ(kmp+ kN)-time algorithm for k-Edit EDSM. Bernardini et al. (Theory of Computing Systems, 2024) presented several algorithms for 1-Approximate EDSM working in Õ(np²+N) time. They have also left the possibility to generalize these solutions for k > 1 as an open problem. We improve the runtime of their solution for 1-Mismatch and 1-Edit EDSM from Õ(np²+N) to 𝒪(np²+N). We further show algorithms for k-Approximate EDSM for the Hamming and edit distances working in Õ(np² + N) time, for any constant k > 0. Finally, we show how our techniques can be applied to improve upon the complexity of the k-Approximate ED String Intersection and k-Approximate Doubly EDSM problems that were introduced very recently by Gabory et al. (Information and Computation, 2025).
Cite as

Solon P. Pissis, Jakub Radoszewski, and Wiktor Zuba. Faster Approximate Elastic-Degenerate String Matching - Part A. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pissis_et_al:LIPIcs.CPM.2025.28,
  author =	{Pissis, Solon P. and Radoszewski, Jakub and Zuba, Wiktor},
  title =	{{Faster Approximate Elastic-Degenerate String Matching - Part A}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{28:1--28:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.28},
  URN =		{urn:nbn:de:0030-drops-231227},
  doi =		{10.4230/LIPIcs.CPM.2025.28},
  annote =	{Keywords: ED string, approximate string matching, Hamming distance, edit distance}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.29
Faster Approximate Elastic-Degenerate String Matching - Part B

Authors: Paweł Gawrychowski, Adam Górkiewicz, Pola Marciniak, Solon P. Pissis, and Karol Pokorski

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of n finite sets of strings of total length N, and compactly describes a collection of strings obtained by first choosing exactly one string in every set, and then concatenating them together. This is motivated by the need of storing a collection of highly similar DNA sequences. The basic algorithmic question on elastic-degenerate strings is pattern matching: given such an elastic-degenerate string and a standard pattern of length m, check if the pattern occurs in one of the strings in the described collection. Bernardini et al. [SICOMP 2022] showed how to leverage fast matrix multiplication to obtain an Õ(nm^{ω-1})+𝒪(N)-time complexity for this problem, where ω is the matrix multiplication exponent. However, from the point of view of possible applications, it is more desirable to work with approximate pattern matching, where we seek approximate occurrences of the pattern. This generalization has been considered in a few papers already, but the best result so far for occurrences with k mismatches, where k is a constant, is the Õ(nm²+N)-time algorithm presented in Part A [CPM 2025]. This brings the question whether increasing the dependency on m from m^{ω-1} to quadratic is necessary when moving from k = 0 to larger (but still constant) k. We design an Õ(nm^{1.5}+N)-time algorithm for pattern matching with k mismatches in an elastic-degenerate string, for any constant k. To obtain this time bound, we leverage the structural characterization of occurrences with k mismatches of Charalampopoulos, Kociumaka, and Wellnitz [FOCS 2020] together with fast Fourier transform. We need to work with multiple patterns at the same time, instead of a single pattern, which requires refining the original characterization. This might be of independent interest.
Cite as

Paweł Gawrychowski, Adam Górkiewicz, Pola Marciniak, Solon P. Pissis, and Karol Pokorski. Faster Approximate Elastic-Degenerate String Matching - Part B. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2025.29,
  author =	{Gawrychowski, Pawe{\l} and G\'{o}rkiewicz, Adam and Marciniak, Pola and Pissis, Solon P. and Pokorski, Karol},
  title =	{{Faster Approximate Elastic-Degenerate String Matching - Part B}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{29:1--29:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.29},
  URN =		{urn:nbn:de:0030-drops-231236},
  doi =		{10.4230/LIPIcs.CPM.2025.29},
  annote =	{Keywords: ED string, approximate pattern matching, Hamming distance, k mismatches}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2023.37
Implementing More Explicit Definitional Expansions in Mizar (Short Paper)

Authors: Adam Grabowski and Artur Korniłowicz

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Abstract
The Mizar language and its corresponding proof-checker offers the tactic of definitional expansions in proof skeletons. This apparatus is rather fragile in the case of intensive overloading of notions (which is widely observed e.g. in the field of algebra, but it is also present in the more fundamental set-theory contexts). We propose the extension of this mechanism: the change should offer users the more precise control over expansions via choosing the right definitional variant for the proof under consideration, still letting the authors to retain the more conservative approach. As a rule, the change will affect new Mizar texts, but obviously, it allows also for solving some context conflicts caused by the original approach in the Mizar repository. The usefulness of our approach is shown by a number of experiments carried out within MML, which is also affected by the change.
Cite as

Adam Grabowski and Artur Korniłowicz. Implementing More Explicit Definitional Expansions in Mizar (Short Paper). In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 37:1-37:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{grabowski_et_al:LIPIcs.ITP.2023.37,
  author =	{Grabowski, Adam and Korni{\l}owicz, Artur},
  title =	{{Implementing More Explicit Definitional Expansions in Mizar}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{37:1--37:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.37},
  URN =		{urn:nbn:de:0030-drops-184121},
  doi =		{10.4230/LIPIcs.ITP.2023.37},
  annote =	{Keywords: Mizar, definitions, proof assistants, mechanization of proof}
}
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