7 Search Results for "Dudek, Bartlomiej"

Document
DOI: 10.4230/LIPIcs.CPM.2023.8
Optimal Near-Linear Space Heaviest Induced Ancestors

Authors: Panagiotis Charalampopoulos, Bartłomiej Dudek, Paweł Gawrychowski, and Karol Pokorski

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)

Abstract
We revisit the Heaviest Induced Ancestors (HIA) problem that was introduced by Gagie, Gawrychowski, and Nekrich [CCCG 2013] and has a number of applications in string algorithms. Let T₁ and T₂ be two rooted trees whose nodes have weights that are increasing in all root-to-leaf paths, and labels on the leaves, such that no two leaves of a tree have the same label. A pair of nodes (u, v) ∈ T₁ × T₂ is induced if and only if there is a label shared by leaf-descendants of u and v. In an HIA query, given nodes x ∈ T₁ and y ∈ T₂, the goal is to find an induced pair of nodes (u, v) of the maximum total weight such that u is an ancestor of x and v is an ancestor of y. Let n be the upper bound on the sizes of the two trees. It is known that no data structure of size 𝒪̃(n) can answer HIA queries in o(log n / log log n) time [Charalampopoulos, Gawrychowski, Pokorski; ICALP 2020]. This (unconditional) lower bound is a polyloglog n factor away from the query time of the fastest 𝒪̃(n)-size data structure known to date for the HIA problem [Abedin, Hooshmand, Ganguly, Thankachan; Algorithmica 2022]. In this work, we resolve the query-time complexity of the HIA problem for the near-linear space regime by presenting a data structure that can be built in 𝒪̃(n) time and answers HIA queries in 𝒪(log n/log log n) time. As a direct corollary, we obtain an 𝒪̃(n)-size data structure that maintains the LCS of a static string and a dynamic string, both of length at most n, in time optimal for this space regime. The main ingredients of our approach are fractional cascading and the utilization of an 𝒪(log n/ log log n)-depth tree decomposition. The latter allows us to break through the Ω(log n) barrier faced by previous works, due to the depth of the considered heavy-path decompositions.
Cite as

Panagiotis Charalampopoulos, Bartłomiej Dudek, Paweł Gawrychowski, and Karol Pokorski. Optimal Near-Linear Space Heaviest Induced Ancestors. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{charalampopoulos_et_al:LIPIcs.CPM.2023.8,
  author =	{Charalampopoulos, Panagiotis and Dudek, Bart{\l}omiej and Gawrychowski, Pawe{\l} and Pokorski, Karol},
  title =	{{Optimal Near-Linear Space Heaviest Induced Ancestors}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.8},
  URN =		{urn:nbn:de:0030-drops-179624},
  doi =		{10.4230/LIPIcs.CPM.2023.8},
  annote =	{Keywords: data structures, string algorithms, fractional cascading}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2020.19
Approximate Majority with Catalytic Inputs

Authors: Talley Amir, James Aspnes, and John Lazarsfeld

Published in: LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)

Abstract
Population protocols [Dana Angluin et al., 2006] are a class of algorithms for modeling distributed computation in networks of finite-state agents communicating through pairwise interactions. Their suitability for analyzing numerous chemical processes has motivated the adaptation of the original population protocol framework to better model these chemical systems. In this paper, we further the study of two such adaptations in the context of solving approximate majority: persistent-state agents (or catalysts) and spontaneous state changes (or leaks). Based on models considered in recent protocols for populations with persistent-state agents [Bartlomiej Dudek and Adrian Kosowski, 2018; Alistarh et al., 2017; Dan Alistarh et al., 2020], we assume a population with n catalytic input agents and m worker agents, and the goal of the worker agents is to compute some predicate over the states of the catalytic inputs. We call this model the Catalytic Input (CI) model. For m = Θ(n), we show that computing the parity of the input population with high probability requires at least Ω(n²) total interactions, demonstrating a strong separation between the CI model and the standard population protocol model. On the other hand, we show that the simple third-state dynamics [Angluin et al., 2008; Perron et al., 2009] for approximate majority in the standard model can be naturally adapted to the CI model: we present such a constant-state protocol for the CI model that solves approximate majority in O(n log n) total steps with high probability when the input margin is Ω(√{n log n}). We then show the robustness of third-state dynamics protocols to the transient leaks events introduced by [Alistarh et al., 2017; Dan Alistarh et al., 2020]. In both the original and CI models, these protocols successfully compute approximate majority with high probability in the presence of leaks occurring at each step with probability β ≤ O(√{n log n}/n). The resilience of these dynamics to leaks exhibits similarities to previous work involving Byzantine agents, and we define and prove a notion of equivalence between the two.
Cite as

Talley Amir, James Aspnes, and John Lazarsfeld. Approximate Majority with Catalytic Inputs. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{amir_et_al:LIPIcs.OPODIS.2020.19,
  author =	{Amir, Talley and Aspnes, James and Lazarsfeld, John},
  title =	{{Approximate Majority with Catalytic Inputs}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Bramas, Quentin and Oshman, Rotem and Romano, Paolo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.19},
  URN =		{urn:nbn:de:0030-drops-135040},
  doi =		{10.4230/LIPIcs.OPODIS.2020.19},
  annote =	{Keywords: population protocols, approximate majority, catalysts, leaks, lower bound}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.23
Counting 4-Patterns in Permutations Is Equivalent to Counting 4-Cycles in Graphs

Authors: Bartłomiej Dudek and Paweł Gawrychowski

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
Permutation σ appears in permutation π if there exists a subsequence of π that is order-isomorphic to σ. The natural algorithmic question is to check if σ appears in π, and if so count the number of occurrences. Only since very recently we know that for any fixed length k, we can check if a given pattern of length k appears in a permutation of length n in time linear in n, but being able to count all such occurrences in f(k)⋅ n^o(k/log k) time would refute the exponential time hypothesis (ETH). Together with practical applications in statistics, this motivates a systematic study of the complexity of counting occurrences for different patterns of fixed small length k. We investigate this question for k = 4. Very recently, Even-Zohar and Leng [arXiv 2019] identified two types of 4-patterns. For the first type they designed an 𝒪̃(n) time algorithm, while for the second they were able to provide an 𝒪̃(n^1.5) time algorithm. This brings up the question whether the permutations of the second type are inherently harder than the first type. We establish a connection between counting 4-patterns of the second type and counting 4-cycles (not necessarily induced) in a sparse undirected graph. By designing two-way reductions we show that the complexities of both problems are the same, up to polylogarithmic factors. This allows us to leverage the work done on the latter to provide a reasonable argument for why there is a difference in the complexities for counting 4-patterns of the first and the second type. In particular, even for the seemingly simpler problem of detecting a 4-cycle in a graph on m edges, the best known algorithm works in 𝒪(m^{4/3}) time. Our reductions imply that an 𝒪(n^{4/3-ε}) time algorithm for counting occurrences of any 4-pattern of the second type in a permutation of length n would imply an exciting breakthrough for counting (and hence also detecting) 4-cycles. In the other direction, by plugging in the fastest known algorithm for counting 4-cycles, we obtain an algorithm for counting occurrences of any 4-pattern of the second type in 𝒪(n^1.48) time.
Cite as

Bartłomiej Dudek and Paweł Gawrychowski. Counting 4-Patterns in Permutations Is Equivalent to Counting 4-Cycles in Graphs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dudek_et_al:LIPIcs.ISAAC.2020.23,
  author =	{Dudek, Bart{\l}omiej and Gawrychowski, Pawe{\l}},
  title =	{{Counting 4-Patterns in Permutations Is Equivalent to Counting 4-Cycles in Graphs}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.23},
  URN =		{urn:nbn:de:0030-drops-133678},
  doi =		{10.4230/LIPIcs.ISAAC.2020.23},
  annote =	{Keywords: Permutations, pattern avoidance, counting cycles}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.18
Generalised Pattern Matching Revisited

Authors: Bartłomiej Dudek, Paweł Gawrychowski, and Tatiana Starikovskaya

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
In the problem of Generalised Pattern Matching (GPM) [STOC'94, Muthukrishnan and Palem], we are given a text T of length n over an alphabet Σ_T, a pattern P of length m over an alphabet Σ_P, and a matching relationship ⊆ Σ_T × Σ_P, and must return all substrings of T that match P (reporting) or the number of mismatches between each substring of T of length m and P (counting). In this work, we improve over all previously known algorithms for this problem: - For ? being the maximum number of characters that match a fixed character, we show two new Monte Carlo algorithms, a reporting algorithm with time ?(? n log n log m) and a (1-ε)-approximation counting algorithm with time ?(ε^-1 ? n log n log m). We then derive a (1-ε)-approximation deterministic counting algorithm for GPM with ?(ε^-2 ? n log⁶ n) time. - For ? being the number of pairs of matching characters, we demonstrate Monte Carlo algorithms for reporting and (1-ε)-approximate counting with running time ?(√? n log m √{log n}) and ?(√{ε^-1 ?} n log m √{log n}), respectively, as well as a (1-ε)-approximation deterministic algorithm for the counting variant of GPM with ?(ε^-1 √{?} n log^{7/2} n) time. - Finally, for ℐ being the total number of disjoint intervals of characters that match the m characters of the pattern P, we show that both the reporting and the counting variants of GPM can be solved exactly and deterministically in ?(n√{ℐ log m} +n log n) time. At the heart of our new deterministic upper bounds for ? and ? lies a faster construction of superimposed codes, which solves an open problem posed in [FOCS'97, Indyk] and can be of independent interest. To conclude, we demonstrate first lower bounds for GPM. We start by showing that any deterministic or Monte Carlo algorithm for GPM must use Ω(?) time, and then proceed to show higher lower bounds for combinatorial algorithms. These bounds show that our algorithms are almost optimal, unless a radically new approach is developed.
Cite as

Bartłomiej Dudek, Paweł Gawrychowski, and Tatiana Starikovskaya. Generalised Pattern Matching Revisited. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dudek_et_al:LIPIcs.STACS.2020.18,
  author =	{Dudek, Bart{\l}omiej and Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  title =	{{Generalised Pattern Matching Revisited}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.18},
  URN =		{urn:nbn:de:0030-drops-118798},
  doi =		{10.4230/LIPIcs.STACS.2020.18},
  annote =	{Keywords: pattern matching, superimposed codes, conditional lower bounds}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.45
Edit Distance between Unrooted Trees in Cubic Time

Authors: Bartlomiej Dudek and Pawel Gawrychowski

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
Edit distance between trees is a natural generalization of the classical edit distance between strings, in which the allowed elementary operations are contraction, uncontraction and relabeling of an edge. Demaine et al. [ACM Trans. on Algorithms, 6(1), 2009] showed how to compute the edit distance between rooted trees on n nodes in O(n^3) time. However, generalizing their method to unrooted trees seems quite problematic, and the most efficient known solution remains to be the previous O(n^3 log n) time algorithm by Klein [ESA 1998]. Given the lack of progress on improving this complexity, it might appear that unrooted trees are simply more difficult than rooted trees. We show that this is, in fact, not the case, and edit distance between unrooted trees on n nodes can be computed in O(n^3) time. A significantly faster solution is unlikely to exist, as Bringmann et al. [SODA 2018] proved that the complexity of computing the edit distance between rooted trees cannot be decreased to O(n^{3-epsilon}) unless some popular conjecture fails, and the lower bound easily extends to unrooted trees. We also show that for two unrooted trees of size m and n, where m <=n, our algorithm can be modified to run in O(nm^2(1+log(n/m))). This, again, matches the complexity achieved by Demaine et al. for rooted trees, who also showed that this is optimal if we restrict ourselves to the so-called decomposition algorithms.
Cite as

Bartlomiej Dudek and Pawel Gawrychowski. Edit Distance between Unrooted Trees in Cubic Time. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 45:1-45:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dudek_et_al:LIPIcs.ICALP.2018.45,
  author =	{Dudek, Bartlomiej and Gawrychowski, Pawel},
  title =	{{Edit Distance between Unrooted Trees in Cubic Time}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{45:1--45:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.45},
  URN =		{urn:nbn:de:0030-drops-90492},
  doi =		{10.4230/LIPIcs.ICALP.2018.45},
  annote =	{Keywords: tree edit distance, dynamic programming, heavy light decomposition}
}
Document
DOI: 10.4230/LIPIcs.CPM.2018.16
Slowing Down Top Trees for Better Worst-Case Compression

Authors: Bartlomiej Dudek and Pawel Gawrychowski

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

Abstract
We consider the top tree compression scheme introduced by Bille et al. [ICALP 2013] and construct an infinite family of trees on n nodes labeled from an alphabet of size sigma, for which the size of the top DAG is Theta(n/log_sigma n log log_sigma n). Our construction matches a previously known upper bound and exhibits a weakness of this scheme, as the information-theoretic lower bound is Omega(n/log_sigma n}). This settles an open problem stated by Lohrey et al. [arXiv 2017], who designed a more involved version achieving the lower bound. We show that this can be also guaranteed by a very minor modification of the original scheme: informally, one only needs to ensure that different parts of the tree are not compressed too quickly. Arguably, our version is more uniform, and in particular, the compression procedure is oblivious to the value of sigma.
Cite as

Bartlomiej Dudek and Pawel Gawrychowski. Slowing Down Top Trees for Better Worst-Case Compression. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 16:1-16:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dudek_et_al:LIPIcs.CPM.2018.16,
  author =	{Dudek, Bartlomiej and Gawrychowski, Pawel},
  title =	{{Slowing Down Top Trees for Better Worst-Case Compression}},
  booktitle =	{29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)},
  pages =	{16:1--16:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-074-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{105},
  editor =	{Navarro, Gonzalo and Sankoff, David and Zhu, Binhai},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2018.16},
  URN =		{urn:nbn:de:0030-drops-86920},
  doi =		{10.4230/LIPIcs.CPM.2018.16},
  annote =	{Keywords: top trees, compression, tree grammars}
}
Document
DOI: 10.4230/LIPIcs.CPM.2017.10
A Family of Approximation Algorithms for the Maximum Duo-Preservation String Mapping Problem

Authors: Bartlomiej Dudek, Pawel Gawrychowski, and Piotr Ostropolski-Nalewaja

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

Abstract
In the Maximum Duo-Preservation String Mapping problem we are given two strings and wish to map the letters of the former to the letters of the latter as to maximise the number of duos. A duo is a pair of consecutive letters that is mapped to a pair of consecutive letters in the same order. This is complementary to the well-studied Minimum Common String Partition problem, where the goal is to partition the former string into blocks that can be permuted and concatenated to obtain the latter string. Maximum Duo-Preservation String Mapping is APX-hard. After a series of improvements, Brubach [WABI 2016] showed a polynomial-time 3.25-approximation algorithm. Our main contribution is that, for any eps>0, there exists a polynomial-time (2+eps)-approximation algorithm. Similarly to a previous solution by Boria et al. [CPM 2016], our algorithm uses the local search technique. However, this is used only after a certain preliminary greedy procedure, which gives us more structure and makes a more general local search possible. We complement this with a specialised version of the algorithm that achieves 2.67-approximation in quadratic time.
Cite as

Bartlomiej Dudek, Pawel Gawrychowski, and Piotr Ostropolski-Nalewaja. A Family of Approximation Algorithms for the Maximum Duo-Preservation String Mapping Problem. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dudek_et_al:LIPIcs.CPM.2017.10,
  author =	{Dudek, Bartlomiej and Gawrychowski, Pawel and Ostropolski-Nalewaja, Piotr},
  title =	{{A Family of Approximation Algorithms for the Maximum Duo-Preservation String Mapping Problem}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{10:1--10:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.10},
  URN =		{urn:nbn:de:0030-drops-73458},
  doi =		{10.4230/LIPIcs.CPM.2017.10},
  annote =	{Keywords: approximation scheme, minimum common string partition, local search}
}
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