21 Search Results for "Equi, Massimo"

Document
DOI: 10.4230/LIPIcs.CPM.2026.7
Optimal Structure for Prefix-Substring Queries

Authors: Paweł Gawrychowski, Florin Manea, and Jonas Richardsen

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

Abstract
The prefix-substring matching problem [Gu, Farach, and Beigel, SODA 1994] consists in preprocessing a string s of length n for the following queries: given a triple (i, j, k) ∈ {0, … , |s|}³ with 1 ≤ j ≤ k, representing a prefix s[1:i] and a substring s[j:k] of s, find the longest prefix of s that is a suffix of s[1:i]s[j:k]. This is an useful primitive in e.g. dynamic text indexing, compressed pattern matching, and pattern matching on block graphs. The border tree uses some basic periodicity properties to answer such queries in 𝒪(log n) time after 𝒪(n) time preprocessing of s. We design a linear-space structure that answers such queries in constant time after 𝒪(n) time preprocessing of s over a polynomial alphabet, which is worst-case optimal.
Cite as

Paweł Gawrychowski, Florin Manea, and Jonas Richardsen. Optimal Structure for Prefix-Substring Queries. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2026.7,
  author =	{Gawrychowski, Pawe{\l} and Manea, Florin and Richardsen, Jonas},
  title =	{{Optimal Structure for Prefix-Substring Queries}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.7},
  URN =		{urn:nbn:de:0030-drops-259333},
  doi =		{10.4230/LIPIcs.CPM.2026.7},
  annote =	{Keywords: Border Tree, Prefix-Substring Query, Data Structures}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.14
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.2026.29
The TAG Array of a Multiple Sequence Alignment

Authors: Jannik Olbrich and Enno Ohlebusch

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

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

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

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@InProceedings{olbrich_et_al:LIPIcs.CPM.2026.29,
  author =	{Olbrich, Jannik and Ohlebusch, Enno},
  title =	{{The TAG Array of a Multiple Sequence Alignment}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{29:1--29:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.29},
  URN =		{urn:nbn:de:0030-drops-259555},
  doi =		{10.4230/LIPIcs.CPM.2026.29},
  annote =	{Keywords: Burrows-Wheeler Transform, pattern matching, index data structure, pangenomics}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.19
Orientation Does Not Help with 3-Coloring a Grid in Online-LOCAL

Authors: Thomas Boudier, Filippo Casagrande, Avinandan Das, Massimo Equi, Henrik Lievonen, Augusto Modanese, and Ronja Stimpert

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
The online-LOCAL and SLOCAL models are extensions of the LOCAL model where nodes are processed in a sequential but potentially adversarial order. So far, the only problem we know of where the global memory of the online-LOCAL model has an advantage over SLOCAL is 3-coloring bipartite graphs. Recently, Chang et al. [PODC 2024] showed that even in grids, 3-coloring requires Ω(log n) locality in deterministic online-LOCAL. This result was subsequently extended by Akbari et al. [STOC 2025] to also hold in randomized online-LOCAL. However, both proofs heavily rely on the assumption that the algorithm does not have access to the orientation of the underlying grid. In this paper, we show how to lift this requirement and obtain the same lower bound (against either model) even when the algorithm is explicitly given a globally consistent orientation of the grid.
Cite as

Thomas Boudier, Filippo Casagrande, Avinandan Das, Massimo Equi, Henrik Lievonen, Augusto Modanese, and Ronja Stimpert. Orientation Does Not Help with 3-Coloring a Grid in Online-LOCAL. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{boudier_et_al:LIPIcs.OPODIS.2025.19,
  author =	{Boudier, Thomas and Casagrande, Filippo and Das, Avinandan and Equi, Massimo and Lievonen, Henrik and Modanese, Augusto and Stimpert, Ronja},
  title =	{{Orientation Does Not Help with 3-Coloring a Grid in Online-LOCAL}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.19},
  URN =		{urn:nbn:de:0030-drops-251925},
  doi =		{10.4230/LIPIcs.OPODIS.2025.19},
  annote =	{Keywords: coloring, locally checkable labeling problems, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.11
New Limits on Distributed Quantum Advantage: Dequantizing Linear Programs

Authors: Alkida Balliu, Corinna Coupette, Antonio Cruciani, Francesco d'Amore, Massimo Equi, Henrik Lievonen, Augusto Modanese, Dennis Olivetti, and Jukka Suomela

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
In this work, we give two results that put new limits on distributed quantum advantage in the context of the LOCAL model of distributed computing: 1) We show that there is no distributed quantum advantage for any linear program. Put otherwise, if there is a quantum-LOCAL algorithm 𝒜 that finds an α-approximation of some linear optimization problem Π in T communication rounds, we can construct a classical, deterministic LOCAL algorithm 𝒜' that finds an α-approximation of Π in T rounds. As a corollary, all classical lower bounds for linear programs, including the KMW bound, hold verbatim in quantum-LOCAL. 2) Using the above result, we show that there exists a locally checkable labeling problem (LCL) for which quantum-LOCAL is strictly weaker than the classical deterministic SLOCAL model. Our results extend from quantum-LOCAL to finitely dependent and non-signaling distributions, and one of the corollaries of our work is that the non-signaling model and the SLOCAL model are incomparable in the context of LCL problems: By prior work, there exists an LCL problem for which SLOCAL is strictly weaker than the non-signaling model, and our work provides a separation in the opposite direction.
Cite as

Alkida Balliu, Corinna Coupette, Antonio Cruciani, Francesco d'Amore, Massimo Equi, Henrik Lievonen, Augusto Modanese, Dennis Olivetti, and Jukka Suomela. New Limits on Distributed Quantum Advantage: Dequantizing Linear Programs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2025.11,
  author =	{Balliu, Alkida and Coupette, Corinna and Cruciani, Antonio and d'Amore, Francesco and Equi, Massimo and Lievonen, Henrik and Modanese, Augusto and Olivetti, Dennis and Suomela, Jukka},
  title =	{{New Limits on Distributed Quantum Advantage: Dequantizing Linear Programs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{11:1--11:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.11},
  URN =		{urn:nbn:de:0030-drops-248280},
  doi =		{10.4230/LIPIcs.DISC.2025.11},
  annote =	{Keywords: linear programming, distributed quantum advantage, quantum-LOCAL model, SLOCAL model, online-LOCAL model, non-signaling distributions, locally checkable labeling problems, dequantization}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.13
Towards Fully Automatic Distributed Lower Bounds

Authors: Alkida Balliu, Sebastian Brandt, Fabian Kuhn, Dennis Olivetti, and Joonatan Saarhelo

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
In the past few years, a successful line of research has led to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level, the round elimination technique can be seen as a recursive application of a function that takes as input a problem Π and outputs a problem Π' that is one round easier than Π. Applying this function recursively to concrete problems of interest can be highly nontrivial, which is one of the reasons that has made the technique difficult to approach. The contribution of our paper is threefold. Firstly, we develop a new and fully automatic method for finding so-called fixed point relaxations under round elimination. The detection of a non-0-round solvable fixed point relaxation of a problem Π immediately implies lower bounds of Ω(log_Δ n) and Ω(log_Δ log n) rounds for deterministic and randomized algorithms for Π, respectively. Secondly, we show that this automatic method is indeed useful, by obtaining lower bounds for defective coloring problems. More precisely, as an application of our procedure, we show that the problem of coloring the nodes of a graph with 3 colors and defect at most (Δ - 3)/2 requires Ω(log_Δ n) rounds for deterministic algorithms and Ω(log_Δ log n) rounds for randomized ones. Additionally, we provide a simplified proof for an existing defective coloring lower bound. We note that lower bounds for coloring problems are notoriously challenging to obtain, both in general, and via the round elimination technique. {Both the first and (indirectly) the second contribution build on our third contribution: a new method to compute the one-round easier problem Π' in the round elimination framework. This method heavily simplifies the usage of the round elimination technique, and in fact it has been successfully exploited in a recent work in order to prove quantum advantage in the distributed setting [STOC '25].}
Cite as

Alkida Balliu, Sebastian Brandt, Fabian Kuhn, Dennis Olivetti, and Joonatan Saarhelo. Towards Fully Automatic Distributed Lower Bounds. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2025.13,
  author =	{Balliu, Alkida and Brandt, Sebastian and Kuhn, Fabian and Olivetti, Dennis and Saarhelo, Joonatan},
  title =	{{Towards Fully Automatic Distributed Lower Bounds}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.13},
  URN =		{urn:nbn:de:0030-drops-248308},
  doi =		{10.4230/LIPIcs.DISC.2025.13},
  annote =	{Keywords: round elimination, lower bounds, defective coloring}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.2
On the Construction of Elastic Degenerate Strings

Authors: Nicola Rizzo, Veli Mäkinen, and Nadia Pisanti

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

Abstract
An elastic degenerate string (EDS) is a sequence of sets of strings. In the context of bioinformatics, EDSes can be used to represent the variations observed in a population from its consensus genome. Pattern matching and comparison problems on EDSes have been widely studied in the literature, but their construction has been largely omitted. We fill this gap by showing how algorithms originally developed for related problems of founder reconstruction can be adapted to minimize the total cardinality of the EDS sets and total length of the EDS strings in linear time, given suitable multiple alignments representing the input data.
Cite as

Nicola Rizzo, Veli Mäkinen, and Nadia Pisanti. On the Construction of Elastic Degenerate Strings. 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. 2:1-2:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rizzo_et_al:OASIcs.Grossi.2,
  author =	{Rizzo, Nicola and M\"{a}kinen, Veli and Pisanti, Nadia},
  title =	{{On the Construction of Elastic Degenerate Strings}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{2:1--2:13},
  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.2},
  URN =		{urn:nbn:de:0030-drops-238014},
  doi =		{10.4230/OASIcs.Grossi.2},
  annote =	{Keywords: multiple sequence alignment, pattern matching, data structures, segmentation algorithms, founder reconstruction, dynamic programming, semi-dynamic range minimum queries, positional Burrows-Wheeler transform}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.7
Conditional Lower Bounds for String Matching in Labelled Graphs

Authors: Massimo Equi

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

Abstract
The problem of String Matching in Labelled Graphs (SMLG) is one possible generalization of the classic problem of finding a string inside another of greater length. In its most general form, SMLG asks to find a match for a string into a graph, which can be directed or undirected. As for string matching, many different variations are possible. For example, the match could be exact or approximate, and the match could lie on a path or a walk. Some of these variations easily fall into the NP-hard realm, while other variants are solvable in polynomial time. For the latter ones, fine-grained complexity has been a game changer in proving quadratic conditional lower bounds, allowing to finally close the gap with those upper bounds that remained unmatched for almost two decades. If the match is allowed to be approximate, SMLG enjoys the same conditional quadratic lower bounds shown for example for edit distance (Backurs and Indyk, STOC '15). The case that really requires ad hoc conditional lower bounds is the one of finding an exact match that lies on a walk. In this work, we focus on explaining various conditional lower bounds for this version of SMLG, with the goal of giving an overall perspective that could help understand which aspects of the problem make it quadratic. We will introduce the reader to the field of fine-grained complexity and show how it can successfully provide the exact type of lower bounds needed for polynomial problems such as SMLG.
Cite as

Massimo Equi. Conditional Lower Bounds for String Matching in Labelled Graphs. 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. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{equi:OASIcs.Grossi.7,
  author =	{Equi, Massimo},
  title =	{{Conditional Lower Bounds for String Matching in Labelled Graphs}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{7:1--7:13},
  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.7},
  URN =		{urn:nbn:de:0030-drops-238063},
  doi =		{10.4230/OASIcs.Grossi.7},
  annote =	{Keywords: conditional lower bounds, strong exponential time hypothesis, fine-grained complexity, string matching, graphs}
}
Document
DOI: 10.4230/OASIcs.Manzini.12
Wheeler Graphs and Wheeler Languages

Authors: Nicola Cotumaccio, Giovanna D'Agostino, Daniel Gibney, Alberto Policriti, Nicola Prezza, and Sharma V. Thankachan

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

Abstract
Suffix sorting stands at the core of the most efficient solutions for indexed pattern matching: the suffix tree, the suffix array, compressed indexes based on the Burrows-Wheeler transform, and so on. In [Gagie, Manzini, Sirén, TCS 2017] this concept was extended to labeled graphs, obtaining the rich class of Wheeler graphs. This work opened a very fruitful line of research, ultimately generating results able to bridge the fields of compressed data structures, graph theory, and regular language theory. In a Wheeler graph, nodes are sorted according to the alphabetic order of their incoming labels, propagating this order through pairs of equally-labeled edges. This apparently-simple definition makes it possible to solve on Wheeler graphs problems (including, but not limited to: compression, subpath queries, NFA equivalence, determinization, minimization) that on general labeled graphs are extremely hard to solve, and induces a rich structure in the class of regular languages (Wheeler languages) recognized by automata whose state transition is a Wheeler graph. The goal of this survey is to provide a summary of (and intuitions behind) the results on Wheeler graphs that appeared in the literature since their introduction, in addition to a discussion of interesting problems that are still open in the field.
Cite as

Nicola Cotumaccio, Giovanna D'Agostino, Daniel Gibney, Alberto Policriti, Nicola Prezza, and Sharma V. Thankachan. Wheeler Graphs and Wheeler Languages. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 12:1-12:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cotumaccio_et_al:OASIcs.Manzini.12,
  author =	{Cotumaccio, Nicola and D'Agostino, Giovanna and Gibney, Daniel and Policriti, Alberto and Prezza, Nicola and Thankachan, Sharma V.},
  title =	{{Wheeler Graphs and Wheeler Languages}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{12:1--12:28},
  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.12},
  URN =		{urn:nbn:de:0030-drops-239205},
  doi =		{10.4230/OASIcs.Manzini.12},
  annote =	{Keywords: Wheeler languages, Wheeler graphs, pattern matching, indexing, compressed data structures}
}
Document
DOI: 10.4230/OASIcs.Manzini.13
Graph Indexing Beyond Wheeler Graphs

Authors: Jarno N. Alanko, Elena Biagi, Massimo Equi, Veli Mäkinen, Simon J. Puglisi, Nicola Rizzo, Kunihiko Sadakane, and Jouni Sirén

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

Abstract
After the discovery of the FM index, which linked the Burrows-Wheeler transform (BWT) to pattern matching on strings, several contemporaneous strands of research began on indexing more complex structures with the BWT, such as tries, finite languages, de Bruijn graphs, and aligned sequences. These directions can now be viewed as culminating in the theory of Wheeler Graphs, but sometimes they go beyond. This chapter reviews the significant body of "proto Wheeler Graph" indexes, many of which exploit characteristics of their specific case to outperform Wheeler graphs, especially in practice.
Cite as

Jarno N. Alanko, Elena Biagi, Massimo Equi, Veli Mäkinen, Simon J. Puglisi, Nicola Rizzo, Kunihiko Sadakane, and Jouni Sirén. Graph Indexing Beyond Wheeler Graphs. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 13:1-13:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alanko_et_al:OASIcs.Manzini.13,
  author =	{Alanko, Jarno N. and Biagi, Elena and Equi, Massimo and M\"{a}kinen, Veli and Puglisi, Simon J. and Rizzo, Nicola and Sadakane, Kunihiko and Sir\'{e}n, Jouni},
  title =	{{Graph Indexing Beyond Wheeler Graphs}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{13:1--13:29},
  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.13},
  URN =		{urn:nbn:de:0030-drops-239215},
  doi =		{10.4230/OASIcs.Manzini.13},
  annote =	{Keywords: indexing, compression, compressed data structures, string algorithms, pattern matching}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.13
Pangenome Graph Indexing via the Multidollar-BWT

Authors: Davide Cozzi, Brian Riccardi, Luca Denti, Simone Ciccolella, Kunihiko Sadakane, and Paola Bonizzoni

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

Abstract
Indexing pangenome graphs is a major algorithmic challenge in computational pangenomics, a recent and active research field that seeks to use graphs as representations of multiple genomes. Since these graphs are constructed from whole genome sequences of a species population, they can become very large, making indexing one of the most challenging problems. In this paper, we propose gindex, a novel indexing approach to solve the Graph Pattern Matching Problem based on the multidollar-BWT. Specifically, gindex aims to find all occurrences of a pattern in a sequence-labeled graph by overcoming two main limitations of GCSA2, one of the most widely used graph indexes: handling queries of arbitrary length and scaling to large graphs without pruning any complex regions. Moreover, we show how a smart preprocessing step can optimize the use of multidollar-BWT to skip small redundant sub-patterns and enhance gindex’s querying capabilities. We demonstrate the effectiveness of our approach by comparing it to GCSA2 in terms of index construction and query time, using different preprocessing modes on three pangenome graphs: one built from Drosophila genomes and two produced by the Human Pangenome Reference Consortium. The results show that gindex can scale on human pangenome graphs - which GCSA2 cannot index using large amounts of RAM - with acceptable memory and time requirements. Moreover, gindex achieves fast query times, although not as fast as GCSA2, which may produce false positives.
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Davide Cozzi, Brian Riccardi, Luca Denti, Simone Ciccolella, Kunihiko Sadakane, and Paola Bonizzoni. Pangenome Graph Indexing via the Multidollar-BWT. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cozzi_et_al:LIPIcs.SEA.2025.13,
  author =	{Cozzi, Davide and Riccardi, Brian and Denti, Luca and Ciccolella, Simone and Sadakane, Kunihiko and Bonizzoni, Paola},
  title =	{{Pangenome Graph Indexing via the Multidollar-BWT}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{13:1--13:17},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-232515},
  doi =		{10.4230/LIPIcs.SEA.2025.13},
  annote =	{Keywords: Multidollar-BWT, Graph Index, Graph Pattern Matching, Pangenome Graph}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.16
Shared Randomness Helps with Local Distributed Problems

Authors: Alkida Balliu, Mohsen Ghaffari, Fabian Kuhn, Augusto Modanese, Dennis Olivetti, Mikaël Rabie, Jukka Suomela, and Jara Uitto

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

Abstract
By prior work, we have many wonderful results related to distributed graph algorithms for problems that can be defined with local constraints; the formal framework used in prior work is locally checkable labeling problems (LCLs), introduced by Naor and Stockmeyer in the 1990s. It is known, for example, that if we have a deterministic algorithm that solves an LCL in o(log n) rounds, we can speed it up to O(log^* n) rounds, and if we have a randomized algorithm that solves an LCL in O(log^* n) rounds, we can derandomize it for free. It is also known that randomness helps with some LCL problems: there are LCL problems with randomized complexity Θ(log log n) and deterministic complexity Θ(log n). However, so far there have not been any LCL problems in which the use of shared randomness has been necessary; in all prior algorithms it has been enough that the nodes have access to their own private sources of randomness. Could it be the case that shared randomness never helps with LCLs? Could we have a general technique that takes any distributed graph algorithm for any LCL that uses shared randomness, and turns it into an equally fast algorithm where private randomness is enough? In this work we show that the answer is no. We present an LCL problem Π such that the round complexity of Π is Ω(√n) in the usual randomized LOCAL model (with private randomness), but if the nodes have access to a source of shared randomness, then the complexity drops to O(log n). As corollaries, we also resolve several other open questions related to the landscape of distributed computing in the context of LCL problems. In particular, problem Π demonstrates that distributed quantum algorithms for LCL problems strictly benefit from a shared quantum state. Problem Π also gives a separation between finitely dependent distributions and non-signaling distributions.
Cite as

Alkida Balliu, Mohsen Ghaffari, Fabian Kuhn, Augusto Modanese, Dennis Olivetti, Mikaël Rabie, Jukka Suomela, and Jara Uitto. Shared Randomness Helps with Local Distributed Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balliu_et_al:LIPIcs.ICALP.2025.16,
  author =	{Balliu, Alkida and Ghaffari, Mohsen and Kuhn, Fabian and Modanese, Augusto and Olivetti, Dennis and Rabie, Mika\"{e}l and Suomela, Jukka and Uitto, Jara},
  title =	{{Shared Randomness Helps with Local Distributed Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{16:1--16:18},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-233931},
  doi =		{10.4230/LIPIcs.ICALP.2025.16},
  annote =	{Keywords: Distributed computing, locally checkable labelings, shared randomness}
}
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)

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@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
DOI: 10.4230/LIPIcs.CPM.2025.1
Representing Paths in Digraphs

Authors: Riccardo Dondi and Alexandru Popa

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

Abstract
In this contribution we consider two combinatorial problems related to graph string matching, motivated by recent approaches in computational genomics. Given a DAG where each node is labeled by a symbol, the problems aim to find a path in the DAG whose nodes contain all (or the maximum number of) symbols of the alphabet. We introduce a decision problem, Σ-Representing Path, that asks whether there exists a path that contains all the symbols of the alphabet, and an optimization problem, called Maximum Representing Path, that asks for a path that contains the maximum number of symbols. We analyze the complexity of the problems, showing the NP-completeness of {Σ-Representing Path} when each symbol labels at most three nodes in the DAG, and showing the APX-hardness of Maximum Representing Path when each symbol labels at most two nodes in the DAG. We complement the first result by giving a polynomial-time algorithm for Σ-Representing Path when each symbol labels at most two nodes in the DAG. Then we investigate the parameterized complexity of the two problems when the DAG has a limited distance from a set of disjoint paths and we show that both problems are W[1]-hard for this parameter. We consider the approximation of Maximum Representing Path, giving an approximation algorithm of factor √OPT, where OPT is the value of an optimal solution of the problem. We also show that Maximum Representing Path cannot be approximated within factor e/(e-1) - α, for any constant α > 0, unless NP ⊆ DTIME(|V|^{O(log log |V|)}) (V is the set of nodes of the DAG).
Cite as

Riccardo Dondi and Alexandru Popa. Representing Paths in Digraphs. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dondi_et_al:LIPIcs.CPM.2025.1,
  author =	{Dondi, Riccardo and Popa, Alexandru},
  title =	{{Representing Paths in Digraphs}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{1:1--1:15},
  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.2025.1},
  URN =		{urn:nbn:de:0030-drops-230954},
  doi =		{10.4230/LIPIcs.CPM.2025.1},
  annote =	{Keywords: Graph String Matching, Computational Complexity, Parameterized Complexity, Algorithms}
}
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