6 Search Results for "Shur, Arseny M."


Document
Searching 2D-Strings for Matching Frames

Authors: Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus, Adrian Miclăuş, and Arseny Shur

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


Abstract
We study a natural type of repetitions in 2-dimensional strings. Such a repetition, called a matching frame, is a rectangular substring of size at least 2× 2 with equal marginal rows and equal marginal columns. Matching frames first appeared in literature in the context of Wang tiles. We present two algorithms finding a matching frame with the maximum perimeter in a given n× m input string. The first algorithm solves the problem exactly in Õ(n^{2.5}) time (assuming n ≥ m). The second algorithm finds a (1-ε)-approximate solution in Õ((nm)/ε⁴) time, which is near linear in the size of the input for constant ε. In particular, by setting ε = O(1) the second algorithm decides the existence of a matching frame in a given string in Õ(nm) time. Some technical elements and structural properties used in these algorithms can be of independent interest.

Cite as

Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus, Adrian Miclăuş, and Arseny Shur. Searching 2D-Strings for Matching Frames. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{boneh_et_al:LIPIcs.CPM.2024.10,
  author =	{Boneh, Itai and Fried, Dvir and Golan, Shay and Kraus, Matan and Micl\u{a}u\c{s}, Adrian and Shur, Arseny},
  title =	{{Searching 2D-Strings for Matching Frames}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.10},
  URN =		{urn:nbn:de:0030-drops-201205},
  doi =		{10.4230/LIPIcs.CPM.2024.10},
  annote =	{Keywords: 2D string, matching frame, LCP, multidimensional range query}
}
Document
Palindromic k-Factorization in Pure Linear Time

Authors: Mikhail Rubinchik and Arseny M. Shur

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)


Abstract
Given a string s of length n over a general alphabet and an integer k, the problem is to decide whether s is a concatenation of k nonempty palindromes. Two previously known solutions for this problem work in time O(kn) and O(nlog n) respectively. Here we settle the complexity of this problem in the word-RAM model, presenting an O(n)-time online deciding algorithm. The algorithm simultaneously finds the minimum odd number of factors and the minimum even number of factors in a factorization of a string into nonempty palindromes. We also demonstrate how to get an explicit factorization of s into k palindromes with an O(n)-time offline postprocessing.

Cite as

Mikhail Rubinchik and Arseny M. Shur. Palindromic k-Factorization in Pure Linear Time. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 81:1-81:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{rubinchik_et_al:LIPIcs.MFCS.2020.81,
  author =	{Rubinchik, Mikhail and Shur, Arseny M.},
  title =	{{Palindromic k-Factorization in Pure Linear Time}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{81:1--81:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.81},
  URN =		{urn:nbn:de:0030-drops-127508},
  doi =		{10.4230/LIPIcs.MFCS.2020.81},
  annote =	{Keywords: stringology, palindrome, palindromic factorization, online algorithm}
}
Document
Searching Long Repeats in Streams

Authors: Oleg Merkurev and Arseny M. Shur

Published in: LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)


Abstract
We consider two well-known related problems: Longest Repeated Substring (LRS) and Longest Repeated Reversed Substring (LRRS). Their streaming versions cannot be solved exactly; we show that only approximate solutions by Monte Carlo algorithms are possible, and prove a lower bound on consumed memory. For both problems, we present purely linear-time Monte Carlo algorithms working in O(E + n/E) space, where E is the additive approximation error. Within the same space bounds, we then present nearly real-time solutions, which require O(log n) time per symbol and O(n + n/E log n) time overall. The working space exactly matches the lower bound whenever E=O(n^{0.5}) and the size of the alphabet is Omega(n^{0.01}).

Cite as

Oleg Merkurev and Arseny M. Shur. Searching Long Repeats in Streams. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{merkurev_et_al:LIPIcs.CPM.2019.31,
  author =	{Merkurev, Oleg and Shur, Arseny M.},
  title =	{{Searching Long Repeats in Streams}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Pisanti, Nadia and P. Pissis, Solon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.31},
  URN =		{urn:nbn:de:0030-drops-105029},
  doi =		{10.4230/LIPIcs.CPM.2019.31},
  annote =	{Keywords: Longest repeated substring, longest repeated reversed substring, streaming algorithm, Karp, Rabin fingerprint, suffix tree}
}
Document
Palindromic Length in Linear Time

Authors: Kirill Borozdin, Dmitry Kosolobov, Mikhail Rubinchik, and Arseny M. Shur

Published in: LIPIcs, Volume 78, 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)


Abstract
Palindromic length of a string is the minimum number of palindromes whose concatenation is equal to this string. The problem of finding the palindromic length drew some attention, and a few O(n log n) time online algorithms were recently designed for it. In this paper we present the first linear time online algorithm for this problem.

Cite as

Kirill Borozdin, Dmitry Kosolobov, Mikhail Rubinchik, and Arseny M. Shur. Palindromic Length in Linear Time. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 23:1-23:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{borozdin_et_al:LIPIcs.CPM.2017.23,
  author =	{Borozdin, Kirill and Kosolobov, Dmitry and Rubinchik, Mikhail and Shur, Arseny M.},
  title =	{{Palindromic Length in Linear Time}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{23:1--23:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{K\"{a}rkk\"{a}inen, Juha and Radoszewski, Jakub and Rytter, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.23},
  URN =		{urn:nbn:de:0030-drops-73389},
  doi =		{10.4230/LIPIcs.CPM.2017.23},
  annote =	{Keywords: palindrome, palindromic length, palindromic factorization, online}
}
Document
On the Size of Lempel-Ziv and Lyndon Factorizations

Authors: Juha Kärkkäinen, Dominik Kempa, Yuto Nakashima, Simon J. Puglisi, and Arseny M. Shur

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)


Abstract
Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct connection between the two by showing that while the Lyndon factorization can be bigger than the non-overlapping LZ factorization (which we demonstrate by describing a new, non-trivial family of strings) it is always less than twice the size.

Cite as

Juha Kärkkäinen, Dominik Kempa, Yuto Nakashima, Simon J. Puglisi, and Arseny M. Shur. On the Size of Lempel-Ziv and Lyndon Factorizations. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 45:1-45:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{karkkainen_et_al:LIPIcs.STACS.2017.45,
  author =	{K\"{a}rkk\"{a}inen, Juha and Kempa, Dominik and Nakashima, Yuto and Puglisi, Simon J. and Shur, Arseny M.},
  title =	{{On the Size of Lempel-Ziv and Lyndon Factorizations}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{45:1--45:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.45},
  URN =		{urn:nbn:de:0030-drops-69878},
  doi =		{10.4230/LIPIcs.STACS.2017.45},
  annote =	{Keywords: Lempel-Ziv factorization, Lempel-Ziv parsing, LZ, Lyndon word, Lyndon factorization, Standard factorization}
}
Document
Tight Tradeoffs for Real-Time Approximation of Longest Palindromes in Streams

Authors: Pawel Gawrychowski, Oleg Merkurev, Arseny Shur, and Przemyslaw Uznanski

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)


Abstract
We consider computing a longest palindrome in the streaming model, where the symbols arrive one-by-one and we do not have random access to the input. While computing the answer exactly using sublinear space is not possible in such a setting, one can still hope for a good approximation guarantee. Our contribution is twofold. First, we provide lower bounds on the space requirements for randomized approximation algorithms processing inputs of length n. We rule out Las Vegas algorithms, as they cannot achieve sublinear space complexity. For Monte Carlo algorithms, we prove a lower bounds of Omega(M log min {|Sigma|, M}) bits of memory; here M=n/E for approximating the answer with additive error E, and M= log n / log (1 + epsilon) for approximating the answer with multiplicative error (1 + epsilon). Second, we design three real-time algorithms for this problem. Our Monte Carlo approximation algorithms for both additive and multiplicative versions of the problem use O(M) words of memory. Thus the obtained lower bounds are asymptotically tight up to a logarithmic factor. The third algorithm is deterministic and finds a longest palindrome exactly if it is short. This algorithm can be run in parallel with a Monte Carlo algorithm to obtain better results in practice. Overall, both the time and space complexity of finding a longest palindrome in a stream are essentially settled.

Cite as

Pawel Gawrychowski, Oleg Merkurev, Arseny Shur, and Przemyslaw Uznanski. Tight Tradeoffs for Real-Time Approximation of Longest Palindromes in Streams. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2016.18,
  author =	{Gawrychowski, Pawel and Merkurev, Oleg and Shur, Arseny and Uznanski, Przemyslaw},
  title =	{{Tight Tradeoffs for Real-Time Approximation of Longest Palindromes in Streams}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.18},
  URN =		{urn:nbn:de:0030-drops-60765},
  doi =		{10.4230/LIPIcs.CPM.2016.18},
  annote =	{Keywords: streaming algorithms, space lower bounds, real-time algorithms, palin- dromes, Monte Carlo algorithms}
}
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