Search Results

Documents authored by Górkiewicz, Adam

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)

Copy BibTex To Clipboard

@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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.93
On Incremental Approximate Shortest Paths in Directed Graphs

Authors: Adam Górkiewicz and Adam Karczmarz

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

Abstract
In this paper, we show new data structures maintaining approximate shortest paths in sparse directed graphs with polynomially bounded non-negative edge weights under edge insertions. We give more efficient incremental (1+ε)-approximate APSP data structures that work against an adaptive adversary: a deterministic one with Õ(m^{3/2}n^{3/4}) total update time and a randomized one with Õ(m^{4/3}n^{5/6}) total update time. For sparse graphs, these both improve polynomially upon the best-known bound against an adaptive adversary [Karczmarz and Łącki, ESA 2019]. To achieve that, building on the ideas of [Chechik and Zhang, SODA 2021] and [Kyng, Meierhans and Probst Gutenberg, SODA 2022], we show a near-optimal (1+ε)-approximate incremental SSSP data structure for a special case when all edge updates are adjacent to the source, that might be of independent interest. We also describe a very simple and near-optimal offline incremental (1+ε)-approximate SSSP data structure. While online near-linear partially dynamic SSSP data structures have been elusive so far (except for dense instances), our result excludes using certain types of impossibility arguments to rule them out. Additionally, our offline solution leads to near-optimal and deterministic all-pairs bounded-leg shortest paths data structure for sparse graphs.
Cite as

Adam Górkiewicz and Adam Karczmarz. On Incremental Approximate Shortest Paths in Directed Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 93:1-93:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{gorkiewicz_et_al:LIPIcs.ICALP.2025.93,
  author =	{G\'{o}rkiewicz, Adam and Karczmarz, Adam},
  title =	{{On Incremental Approximate Shortest Paths in Directed Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{93:1--93:20},
  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.2025.93},
  URN =		{urn:nbn:de:0030-drops-234700},
  doi =		{10.4230/LIPIcs.ICALP.2025.93},
  annote =	{Keywords: dynamic shortest paths, incremental shortest paths, offline dynamic algorithms}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.29
Faster Approximate Elastic-Degenerate String Matching - Part B

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

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

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

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

Copy BibTex To Clipboard

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

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact