21 Search Results for "Köppl, Dominik"

Document
DOI: 10.4230/LIPIcs.WABI.2024.10
b-move: Faster Bidirectional Character Extensions in a Run-Length Compressed Index

Authors: Lore Depuydt, Luca Renders, Simon Van de Vyver, Lennart Veys, Travis Gagie, and Jan Fostier

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract
Due to the increasing availability of high-quality genome sequences, pan-genomes are gradually replacing single consensus reference genomes in many bioinformatics pipelines to better capture genetic diversity. Traditional bioinformatics tools using the FM-index face memory limitations with such large genome collections. Recent advancements in run-length compressed indices like Gagie et al.’s r-index and Nishimoto and Tabei’s move structure, alleviate memory constraints but focus primarily on backward search for MEM-finding. Arakawa et al.’s br-index initiates complete approximate pattern matching using bidirectional search in run-length compressed space, but with significant computational overhead due to complex memory access patterns. We introduce b-move, a novel bidirectional extension of the move structure, enabling fast, cache-efficient bidirectional character extensions in run-length compressed space. It achieves bidirectional character extensions up to 8 times faster than the br-index, closing the performance gap with FM-index-based alternatives, while maintaining the br-index’s favorable memory characteristics. For example, all available complete E. coli genomes on NCBI’s RefSeq collection can be compiled into a b-move index that fits into the RAM of a typical laptop. Thus, b-move proves practical and scalable for pan-genome indexing and querying. We provide a C++ implementation of b-move, supporting efficient lossless approximate pattern matching including locate functionality, available at https://github.com/biointec/b-move under the AGPL-3.0 license.
Cite as

Lore Depuydt, Luca Renders, Simon Van de Vyver, Lennart Veys, Travis Gagie, and Jan Fostier. b-move: Faster Bidirectional Character Extensions in a Run-Length Compressed Index. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{depuydt_et_al:LIPIcs.WABI.2024.10,
  author =	{Depuydt, Lore and Renders, Luca and Van de Vyver, Simon and Veys, Lennart and Gagie, Travis and Fostier, Jan},
  title =	{{b-move: Faster Bidirectional Character Extensions in a Run-Length Compressed Index}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.10},
  URN =		{urn:nbn:de:0030-drops-206546},
  doi =		{10.4230/LIPIcs.WABI.2024.10},
  annote =	{Keywords: Pan-genomics, FM-index, r-index, Move Structure, Bidirectional Search, Approximate Pattern Matching, Lossless Alignment, Cache Efficiency}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.31
Unveiling the Connection Between the Lyndon Factorization and the Canonical Inverse Lyndon Factorization via a Border Property

Authors: Paola Bonizzoni, Clelia De Felice, Brian Riccardi, Rocco Zaccagnino, and Rosalba Zizza

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
The notion of Lyndon word and Lyndon factorization has shown to have unexpected applications in theory as well as in developing novel algorithms on words. A counterpart to these notions are those of inverse Lyndon word and inverse Lyndon factorization. Differently from the Lyndon words, the inverse Lyndon words may be bordered. The relationship between the two factorizations is related to the inverse lexicographic ordering, and has only been recently explored. More precisely, a main open question is how to get an inverse Lyndon factorization from a classical Lyndon factorization under the inverse lexicographic ordering, named CFL_in. In this paper we reveal a strong connection between these two factorizations where the border plays a relevant role. More precisely, we show two main results. We say that a factorization has the border property if a nonempty border of a factor cannot be a prefix of the next factor. First we show that there exists a unique inverse Lyndon factorization having the border property. Then we show that this unique factorization with the border property is the so-called canonical inverse Lyndon factorization, named ICFL. By showing that ICFL is obtained by compacting factors of the Lyndon factorization over the inverse lexicographic ordering, we provide a linear time algorithm for computing ICFL from CFL_in.
Cite as

Paola Bonizzoni, Clelia De Felice, Brian Riccardi, Rocco Zaccagnino, and Rosalba Zizza. Unveiling the Connection Between the Lyndon Factorization and the Canonical Inverse Lyndon Factorization via a Border Property. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bonizzoni_et_al:LIPIcs.MFCS.2024.31,
  author =	{Bonizzoni, Paola and De Felice, Clelia and Riccardi, Brian and Zaccagnino, Rocco and Zizza, Rosalba},
  title =	{{Unveiling the Connection Between the Lyndon Factorization and the Canonical Inverse Lyndon Factorization via a Border Property}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.31},
  URN =		{urn:nbn:de:0030-drops-205879},
  doi =		{10.4230/LIPIcs.MFCS.2024.31},
  annote =	{Keywords: Lyndon words, Lyndon factorization, Combinatorial algorithms on words}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.75
Edit and Alphabet-Ordering Sensitivity of Lex-Parse

Authors: Yuto Nakashima, Dominik Köppl, Mitsuru Funakoshi, Shunsuke Inenaga, and Hideo Bannai

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We investigate the compression sensitivity [Akagi et al., 2023] of lex-parse [Navarro et al., 2021] for two operations: (1) single character edit and (2) modification of the alphabet ordering, and give tight upper and lower bounds for both operations (i.e., we show Θ(log n) bounds for strings of length n). For both lower bounds, we use the family of Fibonacci words. For the bounds on edit operations, our analysis makes heavy use of properties of the Lyndon factorization of Fibonacci words to characterize the structure of lex-parse.
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Yuto Nakashima, Dominik Köppl, Mitsuru Funakoshi, Shunsuke Inenaga, and Hideo Bannai. Edit and Alphabet-Ordering Sensitivity of Lex-Parse. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 75:1-75:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{nakashima_et_al:LIPIcs.MFCS.2024.75,
  author =	{Nakashima, Yuto and K\"{o}ppl, Dominik and Funakoshi, Mitsuru and Inenaga, Shunsuke and Bannai, Hideo},
  title =	{{Edit and Alphabet-Ordering Sensitivity of Lex-Parse}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{75:1--75:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.75},
  URN =		{urn:nbn:de:0030-drops-206314},
  doi =		{10.4230/LIPIcs.MFCS.2024.75},
  annote =	{Keywords: Compression sensitivity, Lex-parse, Fibonacci words}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.9
Top-k Frequent Patterns in Streams and Parameterized-Space LZ Compression

Authors: Patrick Dinklage, Johannes Fischer, and Nicola Prezza

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
We present novel online approximations of the Lempel-Ziv 77 (LZ77) and Lempel-Ziv 78 (LZ78) compression schemes [Lempel & Ziv, 1977/1978] with parameterizable space usage based on estimating which k patterns occur the most frequently in the streamed input for parameter k. This new approach overcomes the issue of finding only local repetitions, which is a natural limitation of algorithms that compress using a sliding window or by partitioning the input into blocks. For this, we introduce the top-k trie, a summary for maintaining online the top-k frequent consecutive patterns in a stream of characters based on a combination of the Lempel-Ziv 78 compression scheme and the Misra-Gries algorithm for frequent item estimation in streams. Using straightforward encoding, our implementations yield compression ratios (output over input size) competitive with established general-purpose LZ-based compression utilities such as gzip or xz.
Cite as

Patrick Dinklage, Johannes Fischer, and Nicola Prezza. Top-k Frequent Patterns in Streams and Parameterized-Space LZ Compression. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dinklage_et_al:LIPIcs.SEA.2024.9,
  author =	{Dinklage, Patrick and Fischer, Johannes and Prezza, Nicola},
  title =	{{Top-k Frequent Patterns in Streams and Parameterized-Space LZ Compression}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.9},
  URN =		{urn:nbn:de:0030-drops-203748},
  doi =		{10.4230/LIPIcs.SEA.2024.9},
  annote =	{Keywords: compression, streaming, heavy hitters, algorithm engineering}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.39
Optimal Bounds for Distinct Quartics

Authors: Panagiotis Charalampopoulos, Paweł Gawrychowski, and Samah Ghazawi

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
A fundamental concept related to strings is that of repetitions. It has been extensively studied in many versions, from both purely combinatorial and algorithmic angles. One of the most basic questions is how many distinct squares, i.e., distinct strings of the form UU, a string of length n can contain as fragments. It turns out that this is always 𝒪(n), and the bound cannot be improved to sublinear in n [Fraenkel and Simpson, JCTA 1998]. Several similar questions about repetitions in strings have been considered, and by now we seem to have a good understanding of their repetitive structure. For higher-dimensional strings, the basic concept of periodicity has been successfully extended and applied to design efficient algorithms - it is inherently more complex than for regular strings. Extending the notion of repetitions and understanding the repetitive structure of higher-dimensional strings is however far from complete. Quartics were introduced by Apostolico and Brimkov [TCS 2000] as analogues of squares in two dimensions. Charalampopoulos, Radoszewski, Rytter, Waleń, and Zuba [ESA 2020] proved that the number of distinct quartics in an n×n 2D string is 𝒪(n²log²n) and that they can be computed in 𝒪(n²log²n) time. Gawrychowski, Ghazawi, and Landau [SPIRE 2021] constructed an infinite family of n×n 2D strings with Ω(n²log n) distinct quartics. This brings the challenge of determining asymptotically tight bounds. Here, we settle both the combinatorial and the algorithmic aspects of this question: the number of distinct quartics in an n×n 2D string is 𝒪(n²log n) and they can be computed in the worst-case optimal 𝒪(n²log n) time. As expected, our solution heavily exploits the periodic structure implied by occurrences of quartics. However, the two-dimensional nature of the problem introduces some technical challenges. Somewhat surprisingly, we overcome the final challenge for the combinatorial bound using a result of Marcus and Tardos [JCTA 2004] for permutation avoidance on matrices.
Cite as

Panagiotis Charalampopoulos, Paweł Gawrychowski, and Samah Ghazawi. Optimal Bounds for Distinct Quartics. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{charalampopoulos_et_al:LIPIcs.ICALP.2024.39,
  author =	{Charalampopoulos, Panagiotis and Gawrychowski, Pawe{\l} and Ghazawi, Samah},
  title =	{{Optimal Bounds for Distinct Quartics}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.39},
  URN =		{urn:nbn:de:0030-drops-201823},
  doi =		{10.4230/LIPIcs.ICALP.2024.39},
  annote =	{Keywords: 2D strings, quartics, repetitions, periodicity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.89
Breaking a Barrier in Constructing Compact Indexes for Parameterized Pattern Matching

Authors: Kento Iseri, Tomohiro I, Diptarama Hendrian, Dominik Köppl, Ryo Yoshinaka, and Ayumi Shinohara

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
A parameterized string (p-string) is a string over an alphabet (Σ_s ∪ Σ_p), where Σ_s and Σ_p are disjoint alphabets for static symbols (s-symbols) and for parameter symbols (p-symbols), respectively. Two p-strings x and y are said to parameterized match (p-match) if and only if x can be transformed into y by applying a bijection on Σ_p to every occurrence of p-symbols in x. The indexing problem for p-matching is to preprocess a p-string T of length n so that we can efficiently find the occurrences of substrings of T that p-match with a given pattern. Let σ_s and respectively σ_p be the numbers of distinct s-symbols and p-symbols that appear in T and σ = σ_s + σ_p. Extending the Burrows-Wheeler Transform (BWT) based index for exact string pattern matching, Ganguly et al. [SODA 2017] proposed parameterized BWTs (pBWTs) to design the first compact index for p-matching, and posed an open problem on how to construct the pBWT-based index in compact space, i.e., in O(n lg |Σ_s ∪ Σ_p|) bits of space. Hashimoto et al. [SPIRE 2022] showed how to construct the pBWT for T, under the assumption that Σ_s ∪ Σ_p = [0..O(σ)], in O(n lg σ) bits of space and O(n (σ_p lg n)/(lg lg n)) time in an online manner while reading the symbols of T from right to left. In this paper, we refine Hashimoto et al.’s algorithm to work in O(n lg σ) bits of space and O(n (lg σ_p lg n)/(lg lg n)) time in a more general assumption that Σ_s ∪ Σ_p = [0..n^{O(1)}]. Our result has an immediate application to constructing parameterized suffix arrays in O(n (lg σ_p lg n)/(lg lg n)) time and O(n lg σ) bits of working space. We also show that our data structure can support backward search, a core procedure of BWT-based indexes, at any stage of the online construction, making it the first compact index for p-matching that can be constructed in compact space and even in an online manner.
Cite as

Kento Iseri, Tomohiro I, Diptarama Hendrian, Dominik Köppl, Ryo Yoshinaka, and Ayumi Shinohara. Breaking a Barrier in Constructing Compact Indexes for Parameterized Pattern Matching. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 89:1-89:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{iseri_et_al:LIPIcs.ICALP.2024.89,
  author =	{Iseri, Kento and I, Tomohiro and Hendrian, Diptarama and K\"{o}ppl, Dominik and Yoshinaka, Ryo and Shinohara, Ayumi},
  title =	{{Breaking a Barrier in Constructing Compact Indexes for Parameterized Pattern Matching}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{89:1--89:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.89},
  URN =		{urn:nbn:de:0030-drops-202324},
  doi =		{10.4230/LIPIcs.ICALP.2024.89},
  annote =	{Keywords: Index for parameterized pattern matching, Parameterized Burrows-Wheeler Transform, Online construction}
}
Document
DOI: 10.4230/LIPIcs.CPM.2024.18
Algorithms for Galois Words: Detection, Factorization, and Rotation

Authors: Diptarama Hendrian, Dominik Köppl, Ryo Yoshinaka, and Ayumi Shinohara

Published in: LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

Abstract
Lyndon words are extensively studied in combinatorics on words - they play a crucial role on upper bounding the number of runs a word can have [Bannai+, SIAM J. Comput.'17]. We can determine Lyndon words, factorize a word into Lyndon words in lexicographically non-increasing order, and find the Lyndon rotation of a word, all in linear time within constant additional working space. A recent research interest emerged from the question of what happens when we change the lexicographic order, which is at the heart of the definition of Lyndon words. In particular, the alternating order, where the order of all odd positions becomes reversed, has been recently proposed. While a Lyndon word is, among all its cyclic rotations, the smallest one with respect to the lexicographic order, a Galois word exhibits the same property by exchanging the lexicographic order with the alternating order. Unfortunately, this exchange has a large impact on the properties Galois words exhibit, which makes it a nontrivial task to translate results from Lyndon words to Galois words. Up until now, it has only been conjectured that linear-time algorithms with constant additional working space in the spirit of Duval’s algorithm are possible for computing the Galois factorization or the Galois rotation. Here, we affirm this conjecture as follows. Given a word T of length n, we can determine whether T is a Galois word, in O(n) time with constant additional working space. Within the same complexities, we can also determine the Galois rotation of T, and compute the Galois factorization of T online. The last result settles Open Problem 1 in [Dolce et al., TCS 2019] for Galois words.
Cite as

Diptarama Hendrian, Dominik Köppl, Ryo Yoshinaka, and Ayumi Shinohara. Algorithms for Galois Words: Detection, Factorization, and Rotation. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hendrian_et_al:LIPIcs.CPM.2024.18,
  author =	{Hendrian, Diptarama and K\"{o}ppl, Dominik and Yoshinaka, Ryo and Shinohara, Ayumi},
  title =	{{Algorithms for Galois Words: Detection, Factorization, and Rotation}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.18},
  URN =		{urn:nbn:de:0030-drops-201288},
  doi =		{10.4230/LIPIcs.CPM.2024.18},
  annote =	{Keywords: Galois Factorization, Alternating Order, Word Factorization Algorithm, Regularity Detection}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.74
Faster Block Tree Construction

Authors: Dominik Köppl, Florian Kurpicz, and Daniel Meyer

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
The block tree [Belazzougui et al. J. Comput. Syst. Sci. '21] is a compressed text index that can answer access (extract a character at a position), rank (number of occurrences of a specified character in a prefix of the text), and select (size of smallest prefix such that a specified character has a specified rank) queries. It requires O(zlog(n/z)) words of space, where z is the number of Lempel-Ziv factors of the text. For some highly repetitive inputs, a block tree can require as little as 0.015 bits per character of the text. Small values of z make the block tree a space-efficient alternative to the wavelet tree, which is another index for these three types of queries. While wavelet trees can be constructed fast in practice, up so far compressed versions of the wavelet tree only leverage statistical compression, meaning that they are blind to spaced repetitions. To make block trees usable in practice, a first step is to find ways in constructing them efficiently. We address this problem by presenting a practically efficient construction algorithm for block trees, which is up to an order of magnitude faster than previous implementations. Additionally, we parallelize our implementation, making it the first block tree construction implementation that works in parallel in shared memory.
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Dominik Köppl, Florian Kurpicz, and Daniel Meyer. Faster Block Tree Construction. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 74:1-74:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{koppl_et_al:LIPIcs.ESA.2023.74,
  author =	{K\"{o}ppl, Dominik and Kurpicz, Florian and Meyer, Daniel},
  title =	{{Faster Block Tree Construction}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{74:1--74:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.74},
  URN =		{urn:nbn:de:0030-drops-187274},
  doi =		{10.4230/LIPIcs.ESA.2023.74},
  annote =	{Keywords: compressed data structure, block tree, Lempel-Ziv compression, longest previous factor array, rank and select}
}
Document
DOI: 10.4230/LIPIcs.WABI.2023.13
Acceleration of FM-Index Queries Through Prefix-Free Parsing

Authors: Aaron Hong, Marco Oliva, Dominik Köppl, Hideo Bannai, Christina Boucher, and Travis Gagie

Published in: LIPIcs, Volume 273, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)

Abstract
FM-indexes are a crucial data structure in DNA alignment, but searching with them usually takes at least one random access per character in the query pattern. Ferragina and Fischer [Ferragina and Fischer, 2007] observed in 2007 that word-based indexes often use fewer random accesses than character-based indexes, and thus support faster searches. Since DNA lacks natural word-boundaries, however, it is necessary to parse it somehow before applying word-based FM-indexing. Last year, Deng et al. [Deng et al., 2022] proposed parsing genomic data by induced suffix sorting, and showed the resulting word-based FM-indexes support faster counting queries than standard FM-indexes when patterns are a few thousand characters or longer. In this paper we show that using prefix-free parsing - which takes parameters that let us tune the average length of the phrases - instead of induced suffix sorting, gives a significant speedup for patterns of only a few hundred characters. We implement our method and demonstrate it is between 3 and 18 times faster than competing methods on queries to GRCh38. And was consistently faster on queries made to 25,000, 50,000 and 100,000 SARS-CoV-2 genomes. Hence, it is very clear that our method accelerates the performance of count over all state-of-the-art methods with a minor increase in the memory.
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Aaron Hong, Marco Oliva, Dominik Köppl, Hideo Bannai, Christina Boucher, and Travis Gagie. Acceleration of FM-Index Queries Through Prefix-Free Parsing. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hong_et_al:LIPIcs.WABI.2023.13,
  author =	{Hong, Aaron and Oliva, Marco and K\"{o}ppl, Dominik and Bannai, Hideo and Boucher, Christina and Gagie, Travis},
  title =	{{Acceleration of FM-Index Queries Through Prefix-Free Parsing}},
  booktitle =	{23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-294-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{273},
  editor =	{Belazzougui, Djamal and Ouangraoua, A\"{i}da},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2023.13},
  URN =		{urn:nbn:de:0030-drops-186390},
  doi =		{10.4230/LIPIcs.WABI.2023.13},
  annote =	{Keywords: FM-index, pangenomics, scalability, word-based indexing, random access}
}
Document
DOI: 10.4230/LIPIcs.CPM.2023.3
Optimal LZ-End Parsing Is Hard

Authors: Hideo Bannai, Mitsuru Funakoshi, Kazuhiro Kurita, Yuto Nakashima, Kazuhisa Seto, and Takeaki Uno

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)

Abstract
LZ-End is a variant of the well-known Lempel-Ziv parsing family such that each phrase of the parsing has a previous occurrence, with the additional constraint that the previous occurrence must end at the end of a previous phrase. LZ-End was initially proposed as a greedy parsing, where each phrase is determined greedily from left to right, as the longest factor that satisfies the above constraint [Kreft & Navarro, 2010]. In this work, we consider an optimal LZ-End parsing that has the minimum number of phrases in such parsings. We show that a decision version of computing the optimal LZ-End parsing is NP-complete by showing a reduction from the vertex cover problem. Moreover, we give a MAX-SAT formulation for the optimal LZ-End parsing adapting an approach for computing various NP-hard repetitiveness measures recently presented by [Bannai et al., 2022]. We also consider the approximation ratio of the size of greedy LZ-End parsing to the size of the optimal LZ-End parsing, and give a lower bound of the ratio which asymptotically approaches 2.
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Hideo Bannai, Mitsuru Funakoshi, Kazuhiro Kurita, Yuto Nakashima, Kazuhisa Seto, and Takeaki Uno. Optimal LZ-End Parsing Is Hard. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 3:1-3:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bannai_et_al:LIPIcs.CPM.2023.3,
  author =	{Bannai, Hideo and Funakoshi, Mitsuru and Kurita, Kazuhiro and Nakashima, Yuto and Seto, Kazuhisa and Uno, Takeaki},
  title =	{{Optimal LZ-End Parsing Is Hard}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{3:1--3:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.3},
  URN =		{urn:nbn:de:0030-drops-179571},
  doi =		{10.4230/LIPIcs.CPM.2023.3},
  annote =	{Keywords: Data Compression, LZ-End, Repetitiveness measures}
}
Document
DOI: 10.4230/LIPIcs.CPM.2023.17
Encoding Hard String Problems with Answer Set Programming

Authors: Dominik Köppl

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)

Abstract
Despite the simple, one-dimensional nature of strings, several computationally hard problems on strings are known. Tackling hard problems beyond sizes of toy instances with straight-forward solutions is infeasible. To solve these problems on datasets of even small sizes, effort has to be put into the conception of algorithms leveraging profound characteristics of the input. Finding these characteristics can be eased by rapidly creating and evaluating prototypes of new concepts in how to tackle hard problems. Such a rapid-prototyping method for hard problems is answer set programming (ASP). In this light, we study the application of ASP on five NP-hard optimization problems in the field of strings. We provide MAX-SAT and ASP encodings, and empirically reason about the merits and flaws when working with ASP solvers.
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Dominik Köppl. Encoding Hard String Problems with Answer Set Programming. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{koppl:LIPIcs.CPM.2023.17,
  author =	{K\"{o}ppl, Dominik},
  title =	{{Encoding Hard String Problems with Answer Set Programming}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{17:1--17:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.17},
  URN =		{urn:nbn:de:0030-drops-179711},
  doi =		{10.4230/LIPIcs.CPM.2023.17},
  annote =	{Keywords: optimization problems, answer set programming, MAX-SAT encoding, NP-hard string problems}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.12
Computing NP-Hard Repetitiveness Measures via MAX-SAT

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

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

Abstract
Repetitiveness measures reveal profound characteristics of datasets, and give rise to compressed data structures and algorithms working in compressed space. Alas, the computation of some of these measures is NP-hard, and straight-forward computation is infeasible for datasets of even small sizes. Three such measures are the smallest size of a string attractor, the smallest size of a bidirectional macro scheme, and the smallest size of a straight-line program. While a vast variety of implementations for heuristically computing approximations exist, exact computation of these measures has received little to no attention. In this paper, we present MAX-SAT formulations that provide the first non-trivial implementations for exact computation of smallest string attractors, smallest bidirectional macro schemes, and smallest straight-line programs. Computational experiments show that our implementations work for texts of length up to a few hundred for straight-line programs and bidirectional macro schemes, and texts even over a million for string attractors.
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Hideo Bannai, Keisuke Goto, Masakazu Ishihata, Shunsuke Kanda, Dominik Köppl, and Takaaki Nishimoto. Computing NP-Hard Repetitiveness Measures via MAX-SAT. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bannai_et_al:LIPIcs.ESA.2022.12,
  author =	{Bannai, Hideo and Goto, Keisuke and Ishihata, Masakazu and Kanda, Shunsuke and K\"{o}ppl, Dominik and Nishimoto, Takaaki},
  title =	{{Computing NP-Hard Repetitiveness Measures via MAX-SAT}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.12},
  URN =		{urn:nbn:de:0030-drops-169505},
  doi =		{10.4230/LIPIcs.ESA.2022.12},
  annote =	{Keywords: repetitiveness measures, string attractor, bidirectional macro scheme}
}
Document
DOI: 10.4230/LIPIcs.CPM.2021.7
Constructing the Bijective and the Extended Burrows-Wheeler Transform in Linear Time

Authors: Hideo Bannai, Juha Kärkkäinen, Dominik Köppl, and Marcin Piątkowski

Published in: LIPIcs, Volume 191, 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)

Abstract
The Burrows-Wheeler transform (BWT) is a permutation whose applications are prevalent in data compression and text indexing. The bijective BWT (BBWT) is a bijective variant of it. Although it is known that the BWT can be constructed in linear time for integer alphabets by using a linear time suffix array construction algorithm, it was up to now only conjectured that the BBWT can also be constructed in linear time. We confirm this conjecture in the word RAM model by proposing a construction algorithm that is based on SAIS, improving the best known result of O(n lg n / lg lg n) time to linear. Since we can reduce the problem of constructing the extended BWT to constructing the BBWT in linear time, we obtain a linear-time algorithm computing the extended BWT at the same time.
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Hideo Bannai, Juha Kärkkäinen, Dominik Köppl, and Marcin Piątkowski. Constructing the Bijective and the Extended Burrows-Wheeler Transform in Linear Time. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bannai_et_al:LIPIcs.CPM.2021.7,
  author =	{Bannai, Hideo and K\"{a}rkk\"{a}inen, Juha and K\"{o}ppl, Dominik and Pi\k{a}tkowski, Marcin},
  title =	{{Constructing the Bijective and the Extended Burrows-Wheeler Transform in Linear Time}},
  booktitle =	{32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-186-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{191},
  editor =	{Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2021.7},
  URN =		{urn:nbn:de:0030-drops-139588},
  doi =		{10.4230/LIPIcs.CPM.2021.7},
  annote =	{Keywords: Burrows-Wheeler Transform, Lyndon words, Circular Suffix Array, Suffix Array Construction Algorithm}
}
Document
DOI: 10.4230/LIPIcs.SEA.2020.7
Fast and Simple Compact Hashing via Bucketing

Authors: Dominik Köppl, Simon J. Puglisi, and Rajeev Raman

Published in: LIPIcs, Volume 160, 18th International Symposium on Experimental Algorithms (SEA 2020)

Abstract
Compact hash tables store a set S of n key-value pairs, where the keys are from the universe U = {0,…,u-1}, and the values are v-bit integers, in close to B(u, n) + nv bits of space, where {b(u, n)} = log₂ binom(u,n) is the information-theoretic lower bound for representing the set of keys in S, and support operations insert, delete and lookup on S. Compact hash tables have received significant attention in recent years, and approaches dating back to Cleary [IEEE T. Comput, 1984], as well as more recent ones have been implemented and used in a number of applications. However, the wins on space usage of these approaches are outweighed by their slowness relative to conventional hash tables. In this paper, we demonstrate that compact hash tables based upon a simple idea of bucketing practically outperform existing compact hash table implementations in terms of memory usage and construction time, and existing fast hash table implementations in terms of memory usage (and sometimes also in terms of construction time). A related notion is that of a compact Hash ID map, which stores a set Ŝ of n keys from U, and implicitly associates each key in Ŝ with a unique value (its ID), chosen by the data structure itself, which is an integer of magnitude O(n), and supports inserts and lookups on Ŝ, while using close to B(u,n) bits. One of our approaches is suitable for use as a compact Hash ID map.
Cite as

Dominik Köppl, Simon J. Puglisi, and Rajeev Raman. Fast and Simple Compact Hashing via Bucketing. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{koppl_et_al:LIPIcs.SEA.2020.7,
  author =	{K\"{o}ppl, Dominik and Puglisi, Simon J. and Raman, Rajeev},
  title =	{{Fast and Simple Compact Hashing via Bucketing}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Faro, Simone and Cantone, Domenico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2020.7},
  URN =		{urn:nbn:de:0030-drops-120817},
  doi =		{10.4230/LIPIcs.SEA.2020.7},
  annote =	{Keywords: compact hashing, hash table, separate chaining}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.21
In-Place Bijective Burrows-Wheeler Transforms

Authors: Dominik Köppl, Daiki Hashimoto, Diptarama Hendrian, and Ayumi Shinohara

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
One of the most well-known variants of the Burrows-Wheeler transform (BWT) [Burrows and Wheeler, 1994] is the bijective BWT (BBWT) [Gil and Scott, arXiv 2012], which applies the extended BWT (EBWT) [Mantaci et al., TCS 2007] to the multiset of Lyndon factors of a given text. Since the EBWT is invertible, the BBWT is a bijective transform in the sense that the inverse image of the EBWT restores this multiset of Lyndon factors such that the original text can be obtained by sorting these factors in non-increasing order. In this paper, we present algorithms constructing or inverting the BBWT in-place using quadratic time. We also present conversions from the BBWT to the BWT, or vice versa, either (a) in-place using quadratic time, or (b) in the run-length compressed setting using 𝒪(n lg r / lg lg r) time with 𝒪(r lg n) bits of words, where r is the sum of character runs in the BWT and the BBWT.
Cite as

Dominik Köppl, Daiki Hashimoto, Diptarama Hendrian, and Ayumi Shinohara. In-Place Bijective Burrows-Wheeler Transforms. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{koppl_et_al:LIPIcs.CPM.2020.21,
  author =	{K\"{o}ppl, Dominik and Hashimoto, Daiki and Hendrian, Diptarama and Shinohara, Ayumi},
  title =	{{In-Place Bijective Burrows-Wheeler Transforms}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.21},
  URN =		{urn:nbn:de:0030-drops-121463},
  doi =		{10.4230/LIPIcs.CPM.2020.21},
  annote =	{Keywords: In-Place Algorithms, Burrows-Wheeler transform, Lyndon words}
}
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