10 Search Results for "Russo, Luís M. S."

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.2026.21
A Bitwise Approach to SCER Matching in Indeterminate Strings

Authors: Simone Faro, Dominik Köppl, Thierry Lecroq, and Francesco Pio Marino

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

Abstract
We study the problem of matching a determinate pattern against an indeterminate text of the same length n, where each text position is a set of possible characters drawn from an alphabet Σ of size σ. We study this matching problem under the order-preserving and parameterized matching setting. For that, we encode character sets by bit expressions using sum-free sequences. This encoding enables constant-time character comparisons and avoids explicit set operations. We present an optimal 𝒪(n) time algorithm for order-preserving matching and an 𝒪(n+(σ_p^x ⋅ σ_p^y) √{σ_p^x + σ_p^y}) time algorithm for parameterized matching, where σ_p^x and σ_p^y denote the number of distinct parameterized symbols in the pattern and the text, respectively. The proposed techniques significantly reduce overhead while maintaining exactness, offering practical performance improvements for pattern matching under uncertainty. Additionally, we extend the parameterized matching framework to allow mismatches, for which we present an algorithm with time complexity 𝒪(σ² n log n + n σ² √σ log(n σ)).
Cite as

Simone Faro, Dominik Köppl, Thierry Lecroq, and Francesco Pio Marino. A Bitwise Approach to SCER Matching in Indeterminate Strings. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{faro_et_al:LIPIcs.CPM.2026.21,
  author =	{Faro, Simone and K\"{o}ppl, Dominik and Lecroq, Thierry and Marino, Francesco Pio},
  title =	{{A Bitwise Approach to SCER Matching in Indeterminate Strings}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{21:1--21:17},
  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.2026.21},
  URN =		{urn:nbn:de:0030-drops-259470},
  doi =		{10.4230/LIPIcs.CPM.2026.21},
  annote =	{Keywords: string matching, indeterminate strings, SCER matching}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.26
Approximate Cartesian Tree Matching with Substitutions

Authors: Panagiotis Charalampopoulos, Jonas Ellert, and Manal Mohamed

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
The Cartesian tree of a sequence captures the relative order of the sequence’s elements. In recent years, Cartesian tree matching has attracted considerable attention, particularly due to its applications in time series analysis. Consider a text T of length n and a pattern P of length m. In the exact Cartesian tree matching problem, the task is to find all length-m fragments of T whose Cartesian tree coincides with the Cartesian tree CT(P) of the pattern. Although the exact version of the problem can be solved in linear time [Park et al., TCS 2020], it remains rather restrictive; for example, it is not robust to outliers in the pattern. To overcome this limitation, we consider the approximate setting, where the goal is to identify all fragments of T that are close to some string whose Cartesian tree matches CT(P). In this work, we quantify closeness via the widely used Hamming distance metric. For a given integer parameter k > 0, we present an algorithm that computes all fragments of T that are at Hamming distance at most k from a string whose Cartesian tree matches CT(P). Our algorithm runs in time 𝒪(n √m ⋅ k^{2.5}) for k ≤ m^{1/5} and in time 𝒪(nk⁵) for k ≥ m^{1/5}, thereby improving upon the state-of-the-art 𝒪(nmk)-time algorithm of Kim and Han [TCS 2025] in the regime k = o(m^{1/4}). On the way to our solution, we develop a toolbox of independent interest. First, we introduce a new notion of periodicity in Cartesian trees. Then, we lift multiple well-known combinatorial and algorithmic results for string matching and periodicity in strings to Cartesian tree matching and periodicity in Cartesian trees.
Cite as

Panagiotis Charalampopoulos, Jonas Ellert, and Manal Mohamed. Approximate Cartesian Tree Matching with Substitutions. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 26:1-26:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charalampopoulos_et_al:LIPIcs.STACS.2026.26,
  author =	{Charalampopoulos, Panagiotis and Ellert, Jonas and Mohamed, Manal},
  title =	{{Approximate Cartesian Tree Matching with Substitutions}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{26:1--26:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.26},
  URN =		{urn:nbn:de:0030-drops-255151},
  doi =		{10.4230/LIPIcs.STACS.2026.26},
  annote =	{Keywords: Cartesian tree, Hamming distance, approximate pattern matching}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.74
Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications

Authors: Paweł Gawrychowski, Egor Gorbachev, and Tomasz Kociumaka

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Min-plus matrix multiplication is a fundamental tool for designing algorithms operating on distances in graphs and different problems solvable by dynamic programming. We know that, assuming the APSP hypothesis, no subcubic-time algorithm exists for the case of general matrices. However, in many applications the matrices admit certain structural properties that can be used to design faster algorithms. For example, when considering a planar graph, one often works with a Monge matrix A, meaning that the density matrix A^◻ has non-negative entries, that is, A^◻_{i,j} := A_{i+1,j} + A_{i,j+1} - A_{i,j} -A_{i+1,j+1} ≥ 0. The min-plus product of two n×n Monge matrices can be computed in 𝒪(n²) time using the famous SMAWK algorithm. In applications such as longest common subsequence, edit distance, and longest increasing subsequence, the matrices are even more structured, as observed by Tiskin [J. Discrete Algorithms, 2008]: they are (or can be converted to) simple unit-Monge matrices, meaning that the density matrix is a permutation matrix and, furthermore, the first column and the last row of the matrix consist of only zeroes. Such matrices admit an implicit representation of size 𝒪(n) and, as shown by Tiskin [SODA 2010 & Algorithmica, 2015], their min-plus product can be computed in 𝒪(nlog n) time. Russo [SPIRE 2010 & Theor. Comput. Sci., 2012] identified a general structural property of matrices that admit such efficient representation and min-plus multiplication algorithms: the core size δ, defined as the number of non-zero entries in the density matrices of the input and output matrices. He provided an adaptive implementation of the SMAWK algorithm that runs in 𝒪((n+δ)log³ n) or 𝒪((n+δ)log² n) time (depending on the representation of the input matrices). In this work, we further investigate the core size as the parameter that enables efficient min-plus matrix multiplication. On the combinatorial side, we provide a (linear) bound on the core size of the product matrix in terms of the core sizes of the input matrices. On the algorithmic side, we generalize Tiskin’s algorithm (but, arguably, with a more elementary analysis) to solve the core-sparse Monge matrix multiplication problem in 𝒪(n+δlog δ) ⊆ 𝒪(n + δ log n) time, matching the complexity for simple unit-Monge matrices. As witnessed by the recent work of Gorbachev and Kociumaka [STOC'25] for edit distance with integer weights, our generalization opens up the possibility of speed-ups for weighted sequence alignment problems. Furthermore, our multiplication algorithm is also capable of producing an efficient data structure for recovering the witness for any given entry of the output matrix. This allows us, for example, to preprocess an integer array of size n in Õ(n) time so that the longest increasing subsequence of any sub-array can be reconstructed in Õ(𝓁) time, where 𝓁 is the length of the reported subsequence. In comparison, Karthik C. S. and Rahul [arXiv, 2024] recently achieved 𝒪(𝓁+n^{1/2}polylog n)-time reporting after 𝒪(n^{3/2}polylog n)-time preprocessing.
Cite as

Paweł Gawrychowski, Egor Gorbachev, and Tomasz Kociumaka. Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 74:1-74:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gawrychowski_et_al:LIPIcs.ESA.2025.74,
  author =	{Gawrychowski, Pawe{\l} and Gorbachev, Egor and Kociumaka, Tomasz},
  title =	{{Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{74:1--74:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.74},
  URN =		{urn:nbn:de:0030-drops-245427},
  doi =		{10.4230/LIPIcs.ESA.2025.74},
  annote =	{Keywords: Min-plus matrix multiplication, Monge matrix, longest increasing subsequence}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.12
Encoding Data Structures for Range Queries on Arrays

Authors: Seungbum Jo and Srinivasa Rao Satti

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
Efficiently processing range queries on arrays is a fundamental problem in computer science, with applications spanning diverse domains such as database management, computational biology, and geographic information systems. A range query retrieves information about a specific segment of an array, such as the sum, minimum, maximum, or median of elements within a given range. The challenge lies in designing data structures that allow such queries to be answered quickly, often in constant or logarithmic time, while keeping space overhead (and preprocessing time) small. Encoding data structures for range queries has emerged as a pivotal area of research due to the increasing demand for high-performance systems handling massive datasets. These structures consider the data together with the queries and aim to store only as much information about the data as is needed to answer the queries. The data structure does not need to access the original data to answer the queries. Encoding-based solutions often leverage techniques from succinct data structures, bit manipulation, and combinatorial optimization to achieve both space and time efficiency. By encoding the array in a manner that preserves critical information, these methods strike a balance between query time and space usage. In this survey article, we explore the landscape of encoding data structures for range queries on arrays, providing a comprehensive overview of some important results on space-efficient encodings for various types of range query.
Cite as

Seungbum Jo and Srinivasa Rao Satti. Encoding Data Structures for Range Queries on Arrays. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 12:1-12:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jo_et_al:OASIcs.Grossi.12,
  author =	{Jo, Seungbum and Satti, Srinivasa Rao},
  title =	{{Encoding Data Structures for Range Queries on Arrays}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{12:1--12:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.12},
  URN =		{urn:nbn:de:0030-drops-238116},
  doi =		{10.4230/OASIcs.Grossi.12},
  annote =	{Keywords: range queries, RMQ, Cartesian tree, top-k queries, range median, range mode}
}
Document
DOI: 10.4230/OASIcs.Manzini.9
Search Schemes for Approximate Pattern Matching: An Overview

Authors: Lore Depuydt, Jan Fostier, Simon Gottlieb, Gregory Kucherov, Knut Reinert, and Luca Renders

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

Abstract
We provide a brief survey of results on solving the approximate pattern matching problem using search schemes, as introduced by Kucherov et al. (2016). We demonstrate that search schemes constitute a flexible and versatile tool that enable the specification of various search strategies, including several known filtering methods. We present approaches for designing efficient search schemes and for implementing them effectively. Finally, we conclude with experimental results comparing multiple search schemes on DNA sequencing data using the Columba software by Renders et al. (2021).
Cite as

Lore Depuydt, Jan Fostier, Simon Gottlieb, Gregory Kucherov, Knut Reinert, and Luca Renders. Search Schemes for Approximate Pattern Matching: An Overview. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{depuydt_et_al:OASIcs.Manzini.9,
  author =	{Depuydt, Lore and Fostier, Jan and Gottlieb, Simon and Kucherov, Gregory and Reinert, Knut and Renders, Luca},
  title =	{{Search Schemes for Approximate Pattern Matching: An Overview}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{9:1--9:16},
  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.9},
  URN =		{urn:nbn:de:0030-drops-239172},
  doi =		{10.4230/OASIcs.Manzini.9},
  annote =	{Keywords: FM-index, bidirectional index, approximate pattern matching, search scheme}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.88
Repetition Aware Text Indexing for Matching Patterns with Wildcards

Authors: Daniel Gibney, Jackson Huffstutler, Mano Prakash Parthasarathi, and Sharma V. Thankachan

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study the problem of indexing a text T[1..n] to support pattern matching with wildcards. The input of a query is a pattern P[1..m] containing h ∈ [0, k] wildcard (a.k.a. don't care) characters and the output is the set of occurrences of P in T (i.e., starting positions of substrings of T that matches P), where k = o(log n) is fixed at index construction. A classic solution by Cole et al. [STOC 2004] provides an index with space complexity O(n ⋅ (clog n)^k/k!)) and query time O(m+2^h log log n+occ), where c > 1 is a constant, and occ denotes the number of occurrences of P in T. We introduce a new data structure that significantly reduces space usage for highly repetitive texts while maintaining efficient query processing. Its space (in words) and query time are as follows: O(δ log (n/δ)⋅ c^k (1+(log^k (δ log n))/k!)) and O((m+2^h +occ)log n)) The parameter δ, known as substring complexity, is a recently introduced measure of repetitiveness that serves as a unifying and lower-bounding metric for several popular measures, including the number of phrases in the LZ77 factorization (denoted by z) and the number of runs in the Burrows-Wheeler Transform (denoted by r). Moreover, O(δ log (n/δ)) represents the optimal space required to encode the data in terms of n and δ, helping us see how close our space is to the minimum required. In another trade-off, we match the query time of Cole et al.’s index using O(n+δ log (n/δ) ⋅ (clogδ)^{k+ε}/k!) space, where ε > 0 is an arbitrarily small constant. We also demonstrate how these techniques can be applied to a more general indexing problem, where the query pattern includes k-gaps (a gap can be interpreted as a contiguous sequence of wildcard characters).
Cite as

Daniel Gibney, Jackson Huffstutler, Mano Prakash Parthasarathi, and Sharma V. Thankachan. Repetition Aware Text Indexing for Matching Patterns with Wildcards. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 88:1-88:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gibney_et_al:LIPIcs.ICALP.2025.88,
  author =	{Gibney, Daniel and Huffstutler, Jackson and Parthasarathi, Mano Prakash and Thankachan, Sharma V.},
  title =	{{Repetition Aware Text Indexing for Matching Patterns with Wildcards}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{88:1--88:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.88},
  URN =		{urn:nbn:de:0030-drops-234656},
  doi =		{10.4230/LIPIcs.ICALP.2025.88},
  annote =	{Keywords: Pattern Matching, Text Indexing, Wildcard Matching}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.13
Quantum Speedup for Sampling Random Spanning Trees

Authors: Simon Apers, Minbo Gao, Zhengfeng Ji, and Chenghua Liu

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We present a quantum algorithm for sampling random spanning trees from a weighted graph in Õ(√{mn}) time, where n and m denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for dense graphs and achieves a quantum speedup over the best-known classical algorithm, which runs in Õ(m) time. The approach carefully combines, on one hand, a classical method based on "large-step" random walks for reduced mixing time and, on the other hand, quantum algorithmic techniques, including quantum graph sparsification and a sampling-without-replacement variant of Hamoudi’s multiple-state preparation. We also establish a matching lower bound, proving the optimality of our algorithm up to polylogarithmic factors. These results highlight the potential of quantum computing in accelerating fundamental graph sampling problems.
Cite as

Simon Apers, Minbo Gao, Zhengfeng Ji, and Chenghua Liu. Quantum Speedup for Sampling Random Spanning Trees. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{apers_et_al:LIPIcs.ICALP.2025.13,
  author =	{Apers, Simon and Gao, Minbo and Ji, Zhengfeng and Liu, Chenghua},
  title =	{{Quantum Speedup for Sampling Random Spanning Trees}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{13:1--13:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.13},
  URN =		{urn:nbn:de:0030-drops-233907},
  doi =		{10.4230/LIPIcs.ICALP.2025.13},
  annote =	{Keywords: Quantum Computing, Quantum Algorithms, Random Spanning Trees}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.27
Succinct Data Structures for Segments

Authors: Philip Bille, Inge Li Gørtz, and Simon R. Tarnow

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

Abstract
We consider succinct data structures for representing a set of n horizontal line segments in the plane given in rank space to support segment access, segment selection, and segment rank queries. A segment access query finds the segment (x₁, x₂, y) given its y-coordinate (y-coordinates of the segments are distinct), a segment selection query finds the jth smallest segment (the segment with the jth smallest y-coordinate) among the segments crossing the vertical line for a given x-coordinate, and a segment rank query finds the number of segments crossing the vertical line through x-coordinate i with y-coordinate at most y, for a given x and y. This problem is a central component in compressed data structures for persistent strings supporting random access. Our main result is a data structure using 2n lg n + O(n lg n / lg lg n) bits of space and O(lg n / lg lg n) query time for all operations. We show that this space bound is optimal up to lower-order terms. We will also show that the query time for segment rank is optimal. The query time for segment selection is also optimal by a previous bound. To obtain our results, we present a novel segment wavelet tree data structure of independent interest. This structure is inspired by and extends the classic wavelet tree for sequences. This leads to a simple, succinct solution with O(log n) query times. We then extend this solution to obtain optimal query time. Our space lower bound follows from a simple counting argument, and our lower bound for segment rank is obtained by a reduction from 2-dimensional counting.
Cite as

Philip Bille, Inge Li Gørtz, and Simon R. Tarnow. Succinct Data Structures for Segments. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bille_et_al:LIPIcs.CPM.2025.27,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and Tarnow, Simon R.},
  title =	{{Succinct Data Structures for Segments}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{27:1--27:14},
  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.2025.27},
  URN =		{urn:nbn:de:0030-drops-231218},
  doi =		{10.4230/LIPIcs.CPM.2025.27},
  annote =	{Keywords: Succinct, Data structures, Selection}
}
Document
DOI: 10.4230/LIPIcs.CPM.2018.2
Order-Preserving Pattern Matching Indeterminate Strings

Authors: Rui Henriques, Alexandre P. Francisco, Luís M. S. Russo, and Hideo Bannai

Published in: LIPIcs, Volume 105, 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)

Abstract
Given an indeterminate string pattern p and an indeterminate string text t, the problem of order-preserving pattern matching with character uncertainties (muOPPM) is to find all substrings of t that satisfy one of the possible orderings defined by p. When the text and pattern are determinate strings, we are in the presence of the well-studied exact order-preserving pattern matching (OPPM) problem with diverse applications on time series analysis. Despite its relevance, the exact OPPM problem suffers from two major drawbacks: 1) the inability to deal with indetermination in the text, thus preventing the analysis of noisy time series; and 2) the inability to deal with indetermination in the pattern, thus imposing the strict satisfaction of the orders among all pattern positions. In this paper, we provide the first polynomial algorithms to answer the muOPPM problem when: 1) indetermination is observed on the pattern or text; and 2) indetermination is observed on both the pattern and the text and given by uncertainties between pairs of characters. First, given two strings with the same length m and O(r) uncertain characters per string position, we show that the muOPPM problem can be solved in O(mr lg r) time when one string is indeterminate and r in N^+ and in O(m^2) time when both strings are indeterminate and r=2. Second, given an indeterminate text string of length n, we show that muOPPM can be efficiently solved in polynomial time and linear space.
Cite as

Rui Henriques, Alexandre P. Francisco, Luís M. S. Russo, and Hideo Bannai. Order-Preserving Pattern Matching Indeterminate Strings. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 2:1-2:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{henriques_et_al:LIPIcs.CPM.2018.2,
  author =	{Henriques, Rui and Francisco, Alexandre P. and Russo, Lu{\'\i}s M. S. and Bannai, Hideo},
  title =	{{Order-Preserving Pattern Matching Indeterminate Strings}},
  booktitle =	{29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)},
  pages =	{2:1--2:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-074-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{105},
  editor =	{Navarro, Gonzalo and Sankoff, David and Zhu, Binhai},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2018.2},
  URN =		{urn:nbn:de:0030-drops-87087},
  doi =		{10.4230/LIPIcs.CPM.2018.2},
  annote =	{Keywords: Order-preserving pattern matching, Indeterminate string analysis, Generic pattern matching, Satisfiability}
}
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