DROPS

Volume

LIPIcs, Volume 54

27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

CPM 2016, June 27-29, 2016, Tel Aviv, Israel

Editors: Roberto Grossi and Moshe Lewenstein

Document

DOI: 10.4230/LIPIcs.STACS.2026.79

Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More

Authors: Mihail Stoian

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

Abstract

Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups. Currently, the only way to repurpose the algorithm of the unweighted version for the weighted version is to employ a polynomial embedding of the input weights. This, however, introduces a pseudo-polynomial factor into the running time, which becomes impractical for arbitrarily weighted instances. In this paper, we introduce a new way to repurpose the algorithm of the unweighted problem. Specifically, we show that the time complexity of several well-known NP-hard problems operating over the (min, +) and (max, +) semirings, such as TSP, Weighted Max-Cut, and Edge-Weighted k-Clique, is proportional to that of their unweighted versions when the set of input weights has small doubling. We achieve this by a meta-algorithm that converts the input weights into polynomially bounded integers using the recent constructive Freiman’s theorem by Randolph and Węgrzycki [ESA 2024] before applying the polynomial embedding.

Cite as

Mihail Stoian. Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{stoian:LIPIcs.STACS.2026.79,
  author =	{Stoian, Mihail},
  title =	{{Mind the Gap. Doubling Constant Parametrization of Weighted Problems: TSP, Max-Cut, and More}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{79:1--79:19},
  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.2026.79},
  URN =		{urn:nbn:de:0030-drops-255680},
  doi =		{10.4230/LIPIcs.STACS.2026.79},
  annote =	{Keywords: doubling constant parametrization, weighted problems, traveling salesman, weighted max-cut, edge-weighted k-clique}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.62

Relative Compressed Reverse Suffix Array

Authors: Muhammed Oguzhan Kulekci, Mano Prakash Parthasarathi, Rahul Shah, and Sharma V. Thankachan

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

Abstract

Suffix trees and suffix arrays are two fundamental data structures in the field of string algorithms. For a string (a.k.a. text or sequence) of length n over an alphabet of size σ, these structures typically require O(nlog n) bits of space. The FM-index provides a compressed representation of the suffix array in ≈ nlog σ bits, allowing for efficient queries on both the suffix array and its inverse array in near logarithmic time. In certain applications, such as approximate pattern matching (i.e., with wildcards, mismatches, edits), there is a need to access the suffix array of a text, as well as the suffix array of text’s reverse. Motivated by this, we explore the possibility of encoding the suffix array of the reversed text in a compact form, assuming the availability of the FM-index for the original text. Our first solution is an O(n)-bit (relative) encoding of the suffix array of the reversed text, with the time for decoding an entry being only O(log^*n) times that of decoding an entry in the text’s suffix array using FM-index. We then demonstrate how to reduce the space to O(n/κ) bits for a parameter κ, while multiplicative factor in time becomes approximately O(κlog^*n+κ³). We can also support inverse suffix array and longest common extension queries on the reversed text. These results are achieved through some careful and non-trivial application of various succinct data structure techniques.

Cite as

Muhammed Oguzhan Kulekci, Mano Prakash Parthasarathi, Rahul Shah, and Sharma V. Thankachan. Relative Compressed Reverse Suffix Array. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 62:1-62:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kulekci_et_al:LIPIcs.STACS.2026.62,
  author =	{Kulekci, Muhammed Oguzhan and Parthasarathi, Mano Prakash and Shah, Rahul and Thankachan, Sharma V.},
  title =	{{Relative Compressed Reverse Suffix Array}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{62:1--62:21},
  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.2026.62},
  URN =		{urn:nbn:de:0030-drops-255512},
  doi =		{10.4230/LIPIcs.STACS.2026.62},
  annote =	{Keywords: String Matching, Text Indexing, Data Structures, Suffix Trees}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.68

Dynamic Pattern Matching with Wildcards

Authors: Arshia Ataee Naeini, Amir-Parsa Mobed, Masoud Seddighin, and Saeed Seddighin

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

Abstract

We study the fully dynamic pattern matching problem where the pattern may contain up to k wildcard symbols, each matching any symbol of the alphabet. Both the text and the pattern are subject to updates (insert, delete, change). We design an algorithm with 𝒪(n log² n) preprocessing and update/query time 𝒪̃(kn^{k/{k+1}} + k² log n). The bound is truly sublinear for a constant k, and sublinear when k = o(log n). We further complement our results with a conditional lower bound: assuming subquadratic preprocessing time, achieving truly sublinear update time for the case k = Ω(log n) would contradict the Strong Exponential Time Hypothesis (SETH). Finally, we develop sublinear algorithms for two special cases: - If the pattern contains w non-wildcard symbols, we give an algorithm with preprocessing time 𝒪(nw) and update time 𝒪(w + log n), which is truly sublinear whenever w is truly sublinear. - Using FFT technique combined with block decomposition, we design a deterministic truly sublinear algorithm with preprocessing time 𝒪(n^{1.8}) and update time 𝒪(n^{0.8} log n) for the case that there are at most two non-wildcards.

Cite as

Arshia Ataee Naeini, Amir-Parsa Mobed, Masoud Seddighin, and Saeed Seddighin. Dynamic Pattern Matching with Wildcards. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 68:1-68:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{naeini_et_al:LIPIcs.STACS.2026.68,
  author =	{Naeini, Arshia Ataee and Mobed, Amir-Parsa and Seddighin, Masoud and Seddighin, Saeed},
  title =	{{Dynamic Pattern Matching with Wildcards}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{68:1--68:20},
  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.2026.68},
  URN =		{urn:nbn:de:0030-drops-255579},
  doi =		{10.4230/LIPIcs.STACS.2026.68},
  annote =	{Keywords: pattern matching, wildcards, dynamic algorithms, string algorithms, data structures}
}

Document

DOI: 10.4230/LIPIcs.ESA.2025.54

Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems

Authors: Bingbing Hu and Adam Polak

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

Abstract

Most of the known tight lower bounds for dynamic problems are based on the Online Boolean Matrix-Vector Multiplication (OMv) Hypothesis, which is not as well studied and understood as some more popular hypotheses in fine-grained complexity. It would be desirable to base hardness of dynamic problems on a more believable hypothesis. We propose analogues of the OMv Hypothesis for variants of matrix multiplication that are known to be harder than Boolean product in the offline setting, namely: equality, dominance, min-witness, min-max, and bounded monotone min-plus products. These hypotheses are a priori weaker assumptions than the standard (Boolean) OMv Hypothesis and yet we show that they are actually equivalent to it. This establishes the first such fine-grained equivalence class for dynamic problems.

Cite as

Bingbing Hu and Adam Polak. Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hu_et_al:LIPIcs.ESA.2025.54,
  author =	{Hu, Bingbing and Polak, Adam},
  title =	{{Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{54:1--54:16},
  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.2025.54},
  URN =		{urn:nbn:de:0030-drops-245228},
  doi =		{10.4230/LIPIcs.ESA.2025.54},
  annote =	{Keywords: Fine-grained complexity, OMv hypothesis, reductions, equivalence class}
}

Document

DOI: 10.4230/LIPIcs.ESA.2025.33

Better Indexing for Rectangular Pattern Matching

Authors: Paweł Gawrychowski and Adam Górkiewicz

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

Abstract

We revisit the complexity of building, given a two-dimensional string of size n, an indexing structure that allows locating all k occurrences of a two-dimensional pattern of size m. While a structure of size 𝒪(n) with query time 𝒪(m+k) is known for this problem under the additional assumption that the pattern is a square [Giancarlo, SICOMP 1995], a popular belief was that for rectangular patterns one cannot achieve such (or even similar) bounds, due to a lower bound for a certain natural class of approaches [Giancarlo, WADS 1993]. We show that, in fact, it is possible to construct a very simple structure of size 𝒪(nlog n) that supports such queries for any rectangular pattern in 𝒪(m+klog^{ε}n) time, for any ε > 0.

Cite as

Paweł Gawrychowski and Adam Górkiewicz. Better Indexing for Rectangular Pattern Matching. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 33:1-33:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gawrychowski_et_al:LIPIcs.ESA.2025.33,
  author =	{Gawrychowski, Pawe{\l} and G\'{o}rkiewicz, Adam},
  title =	{{Better Indexing for Rectangular Pattern Matching}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{33:1--33:7},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-245011},
  doi =		{10.4230/LIPIcs.ESA.2025.33},
  annote =	{Keywords: 2D strings, pattern matching, string indexing}
}

Document

DOI: 10.4230/LIPIcs.ESA.2025.72

Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions

Authors: Noam Horowicz and Tsvi Kopelowitz

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

Abstract

In the snippets problem, the goal is to preprocess a text T so that given two pattern queries, P₁ and P₂, one can quickly locate the occurrences of the two patterns in T that are closest to each other, or report the distance between these occurrences. Kopelowitz and Krauthgamer [CPM2016] showed upper bound tradeoffs and conditional lower bounds tradeoffs for the snippets problem, by utilizing connections between the snippets problem and the problem of constructing a color distance oracle (CDO), which is a data structure that preprocess a set of points with associated colors so that given two colors c and c' one can quickly find the (distance between the) closest pair of points where one has color c and the other has color c'. However, the existing upper bound and lower bound curves are not tight. Inspired by recent advances by Kopelowitz and Vassilevska-Williams [ICALP2020] regarding tradeoff curves for Set-disjointness data structures, in this paper we introduce new conditionally optimal algorithms for a (1+ε) approximation version of the snippets problem and a (1+ε) approximation version of the CDO problem, by applying fast matrix multiplication. For example, for CDO on n points in an array, if the preprocessing time is Õ(n^a) and the query time is Õ(n^b) then, assuming that ω = 2 (where ω is the exponent of n in the runtime of the fastest matrix multiplication algorithm on two squared matrices of size n× n), we show that approximate CDO can be solved with the following tradeoff a + 2b = 2 (if 0 ≤ b ≤ 1/3) 2a + b = 3 (if 1/3 ≤ b ≤ 1). Moreover, we prove that for exact CDO on points in an array, the algorithm of Kopelowitz and Krauthgamer [CPM2016], which obtains a tradeoff of a+b = 2, is essentially optimal assuming that the strong all-pairs shortest paths hypothesis holds for randomized algorithms. Thus, we demonstrate that the exact version of CDO is strictly harder than the approximate version. Moreover, this separation carries over to the snippets problem.

Cite as

Noam Horowicz and Tsvi Kopelowitz. Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 72:1-72:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{horowicz_et_al:LIPIcs.ESA.2025.72,
  author =	{Horowicz, Noam and Kopelowitz, Tsvi},
  title =	{{Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{72:1--72:17},
  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.2025.72},
  URN =		{urn:nbn:de:0030-drops-245403},
  doi =		{10.4230/LIPIcs.ESA.2025.72},
  annote =	{Keywords: data structures, fast matrix multiplication, fine-grained complexity, pattern matching, distance oracles}
}

Document

DOI: 10.4230/LIPIcs.ESA.2025.60

Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars

Authors: Jannik Olbrich

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

Abstract

The Burrows-Wheeler Transform (BWT) serves as the basis for many important sequence indexes. On very large datasets (e.g. genomic databases), classical BWT construction algorithms are often infeasible because they usually need to have the entire dataset in main memory. Fortunately, such large datasets are often highly repetitive. It can thus be beneficial to compute the BWT from a compressed representation. We propose an algorithm for computing the BWT via the Lyndon straight-line program, a grammar based on the standard factorization of Lyndon words. Our algorithm can also be used to compute the extended BWT (eBWT) of a multiset of sequences. We empirically evaluate our implementation and find that we can compute the BWT and eBWT of very large datasets faster and/or with less memory than competing methods.

Cite as

Jannik Olbrich. Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 60:1-60:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{olbrich:LIPIcs.ESA.2025.60,
  author =	{Olbrich, Jannik},
  title =	{{Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{60:1--60:19},
  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.2025.60},
  URN =		{urn:nbn:de:0030-drops-245286},
  doi =		{10.4230/LIPIcs.ESA.2025.60},
  annote =	{Keywords: Burrows-Wheeler Transform, Grammar compression}
}

Document

DOI: 10.4230/LIPIcs.WADS.2025.30

Convolution and Knapsack in Higher Dimensions

Authors: Kilian Grage, Klaus Jansen, and Björn Schumacher

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract

In the Knapsack problem, one is given the task of packing a knapsack of a given size with items in order to gain a packing with a high profit value. As one of the most classical problems in computer science, research for this problem has gone a long way. One important connection to the (max,+)-convolution problem has been established, where knapsack solutions can be combined by building the convolution of two sequences. This observation has been used in recent years to give conditional lower bounds but also parameterized algorithms. In this paper we carry these results into higher dimensions. We consider Knapsack where items are characterized by multiple properties - given through a vector - and a knapsack that has a capacity vector. The packing must not exceed any of the given capacity constraints. In order to show a similar sub-quadratic lower bound we consider a multidimensional version of (max, +)-convolution. We then consider variants of this problem introduced by Cygan et al. and prove that they are all equivalent in terms of algorithms that allow for a running time sub-quadratic in the number of entries of the array. We further develop a parameterized algorithm to solve higher dimensional Knapsack. The techniques we apply are inspired by an algorithm introduced by Axiotis and Tzamos. We will show that even for higher dimensional Knapsack, we can reduce the problem to convolution on one-dimensional, concave sequences, leading to an 𝒪(dn + dD ⋅ max{(Π_{i=1}^d t_i), t_max log t_max}) algorithm, where D is the number of different weight vectors, t the capacity vector and d is the dimension of the problem. Then, we use the techniques to improve the approach of Eisenbrand and Weismantel to obtain an algorithm for Integer Linear Programming with upper bounds with running time 𝒪(dn) + D ⋅ 𝒪(d Δ)^{d(d+1)} + T_LP. Finally, we give an divide-and-conquer algorithm for ILP with running time n^{d+1} ⋅ O(Δ)^d ⋅ log(|u - 𝓁|_∞).

Cite as

Kilian Grage, Klaus Jansen, and Björn Schumacher. Convolution and Knapsack in Higher Dimensions. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grage_et_al:LIPIcs.WADS.2025.30,
  author =	{Grage, Kilian and Jansen, Klaus and Schumacher, Bj\"{o}rn},
  title =	{{Convolution and Knapsack in Higher Dimensions}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.30},
  URN =		{urn:nbn:de:0030-drops-242618},
  doi =		{10.4230/LIPIcs.WADS.2025.30},
  annote =	{Keywords: Knapsack, Convolution, Integer Linear Programming}
}

Document

DOI: 10.4230/LIPIcs.WADS.2025.35

Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage

Authors: Meng He and Kaiyu Wu

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract

We improve the recent succinct data structure result of Balakrishnan et al. for chordal graphs with bounded vertex leafage (SWAT 2024). A chordal graph is a widely studied graph class which can be characterized as the intersection graph of subtrees of a host tree, denoted as a tree representation of the chordal graph. The vertex leafage and leafage parameters of a chordal graph deal with the existence of a tree representation with a bounded number of leaves in either the subtrees representing the vertices or the host tree itself. We simplify the lower bound proof of Balakrishnan et al. which applied to only chordal graphs with bounded vertex leafage, and extend it to a lower bound proof for chordal graphs with bounded leafage as well. For both classes of graphs, the information-theoretic lower bound we (re-)obtain for k = o(n) is (k-1)nlog n - knlog k - o(knlog n) bits, where the leafage or vertex leafage of the graph is at most k = o(n). We further extend the range of the parameter k to Θ(n) as well. Then we give a succinct data structure using (k-1)nlog (n/k) + o(knlog n) bits to answer adjacent queries, which test the adjacency between pairs of vertices, in O((log k)/(log log n) + 1) time compared to the O(klog n) time of the data structure of Balakrishnan et al. For the neighborhood query which lists the neighbours of a given vertex, our query time is O((log n)/(log log n)) per neighbour compared to O(k²log n) per neighbour. We also extend the data structure ideas to obtain a succinct data structure for chordal graphs with bounded leafage k, answering an open question of Balakrishnan et al. Our succinct data structure, which uses (k-1)nlog (n/k) + o(knlog n) bits, has query time O(1) for the adjacent query and O(1) per neighbour for the neighborhood query. Using slightly more space (an additional (1+ε)nlog n bits for any ε > 0) allows distance queries, which compute the number of edges in the shortest path between two given vertices, to be answered in O(1) time as well.

Cite as

Meng He and Kaiyu Wu. Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{he_et_al:LIPIcs.WADS.2025.35,
  author =	{He, Meng and Wu, Kaiyu},
  title =	{{Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{35:1--35:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.35},
  URN =		{urn:nbn:de:0030-drops-242660},
  doi =		{10.4230/LIPIcs.WADS.2025.35},
  annote =	{Keywords: Chordal Graph, Leafage, Vertex Leafage, Succinct Data Structure}
}

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

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

Research

DOI: 10.4230/OASIcs.Grossi.16

Faster Range LCP Queries in Linear Space

Authors: Yakov Nekirch and Sharma V. Thankachan

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

Abstract

A range LCP query rlcp(α,β) on a text T[1 .. n] asks to return the length of the longest common prefix of any two suffixes of T with starting positions in a range [α,β]. In this paper we describe a data structure that uses O(n) space and supports range LCP queries in time O(log^ε n) for any constant ε > 0. Our result is the fastest currently known linear-space solution for this problem.

Cite as

Yakov Nekirch and Sharma V. Thankachan. Faster Range LCP Queries in Linear Space. 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. 16:1-16:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nekirch_et_al:OASIcs.Grossi.16,
  author =	{Nekirch, Yakov and Thankachan, Sharma V.},
  title =	{{Faster Range LCP Queries in Linear Space}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{16:1--16:6},
  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.16},
  URN =		{urn:nbn:de:0030-drops-238158},
  doi =		{10.4230/OASIcs.Grossi.16},
  annote =	{Keywords: Data Structures, String Algorithms, Longest Common Prefix}
}

Document

DOI: 10.4230/OASIcs.Manzini.2

A Survey of the Bijective Burrows-Wheeler Transform

Authors: Hideo Bannai, Dominik Köppl, and Zsuzsanna Lipták

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

Abstract

The Bijective BWT (BBWT), conceived by Scott in 2007, later summarized in a preprint by Gil and Scott in 2009 (arXiv 2012), is a variant of the Burrows-Wheeler Transform which is bijective: every string is the BBWT of some string. Indeed, the BBWT of a string is the extended BWT [Mantaci et al., 2007] of the factors of its Lyndon factorization. The BBWT has been receiving increasing interest in recent years. In this paper, we survey existing research on the BBWT, starting with its history and motivation. We then present algorithmic topics including construction algorithms with various complexities and an index on top of the BBWT for pattern matching. We subsequently address some properties of the BBWT as a compressor, discussing robustness to operations such as reversal, edits, rotation, as well as compression power. We close with listing other bijective variants of the BWT and open problems concerning the BBWT.

Cite as

Hideo Bannai, Dominik Köppl, and Zsuzsanna Lipták. A Survey of the Bijective Burrows-Wheeler Transform. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 2:1-2:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bannai_et_al:OASIcs.Manzini.2,
  author =	{Bannai, Hideo and K\"{o}ppl, Dominik and Lipt\'{a}k, Zsuzsanna},
  title =	{{A Survey of the Bijective Burrows-Wheeler Transform}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{2:1--2:26},
  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.2},
  URN =		{urn:nbn:de:0030-drops-239100},
  doi =		{10.4230/OASIcs.Manzini.2},
  annote =	{Keywords: Burrows-Wheeler Transform, compression, text indexing, repetitiveness measure, Lyndon words, index construction algorithms, bijective string transformation}
}

Document

DOI: 10.4230/OASIcs.Manzini.11

Circular Dictionary Matching Using Extended BWT

Authors: Wing-Kai Hon, Rahul Shah, 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

The dictionary matching problem involves preprocessing a set of strings (patterns) into a data structure that efficiently identifies all occurrences of these patterns within a query string (text). In this work, we investigate a variation of this problem, termed circular dictionary matching, where the patterns are circular, meaning their cyclic shifts are also considered valid patterns. Such patterns naturally occur in areas such as bioinformatics and computational geometry. Based on the extended Burrows-Wheeler Transformation (eBWT), we design a space-efficient solution for this problem. Specifically, we show that a dictionary of d circular patterns of total length n can be indexed in nlog σ + O(n+dlog n+σ log n) bits of space and support circular dictionary matching on a query text T in O((|T|+occ)log n) time, where σ represents the size of the underlying alphabet and occ represents the output size.

Cite as

Wing-Kai Hon, Rahul Shah, and Sharma V. Thankachan. Circular Dictionary Matching Using Extended BWT. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hon_et_al:OASIcs.Manzini.11,
  author =	{Hon, Wing-Kai and Shah, Rahul and Thankachan, Sharma V.},
  title =	{{Circular Dictionary Matching Using Extended BWT}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{11:1--11:14},
  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.11},
  URN =		{urn:nbn:de:0030-drops-239195},
  doi =		{10.4230/OASIcs.Manzini.11},
  annote =	{Keywords: String algorithms, Burrows-Wheeler transformation, suffix trees, succinct data structures}
}

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