4 Search Results for "Wygocki, Piotr"

Document
DOI: 10.4230/LIPIcs.IPEC.2025.17
Treedepth Inapproximability and Exponential ETH Lower Bound

Authors: Édouard Bonnet, Daniel Neuen, and Marek Sokołowski

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Treedepth is a central parameter to algorithmic graph theory. The current state-of-the-art in computing and approximating treedepth consists of a 2^{O(k²)} n-time exact algorithm and a polynomial-time O(OPT log^{3/2} OPT)-approximation algorithm, where the former algorithm returns an elimination forest of height k (witnessing that treedepth is at most k) for the n-vertex input graph G, or correctly reports that G has treedepth larger than k, and OPT is the actual value of the treedepth. On the complexity side, exactly computing treedepth is NP-complete, but the known reductions do not rule out a polynomial-time approximation scheme (PTAS), and under the Exponential Time Hypothesis (ETH) only exclude a running time of 2^o(√n) for exact algorithms. We show that 1.0003-approximating Treedepth is NP-hard, and that exactly computing the treedepth of an n-vertex graph requires time 2^Ω(n), unless the ETH fails. We further derive that there exist absolute constants δ, c > 0 such that any (1+δ)-approximation algorithm requires time 2^Ω(n/log^c n). We do so via a simple direct reduction from Satisfiability to Treedepth, inspired by a reduction recently designed for Treewidth [STOC '25].
Cite as

Édouard Bonnet, Daniel Neuen, and Marek Sokołowski. Treedepth Inapproximability and Exponential ETH Lower Bound. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 17:1-17:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonnet_et_al:LIPIcs.IPEC.2025.17,
  author =	{Bonnet, \'{E}douard and Neuen, Daniel and Soko{\l}owski, Marek},
  title =	{{Treedepth Inapproximability and Exponential ETH Lower Bound}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{17:1--17:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.17},
  URN =		{urn:nbn:de:0030-drops-251494},
  doi =		{10.4230/LIPIcs.IPEC.2025.17},
  annote =	{Keywords: treedepth, lower bounds, approximation}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.32
The PACE 2025 Parameterized Algorithms and Computational Experiments Challenge: Dominating Set and Hitting Set

Authors: Mario Grobler and Sebastian Siebertz

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
The 10th iteration of the of the Parameterized Algorithms and Computational Experiments challenge (PACE) 2025 was devoted to engineer algorithms solving the Dominating Set problem as well as the Hitting Set problem. In contrast to the last iterations, these problems are (under standard assumptions) not fixed-parameter tractable (fpt) in general. However, restricting the structure of the input (e.g. to planar graphs or degenerate graphs for Dominating Set, or to set systems with sets of bounded size for Hitting Set) renders these problems fpt. Following the spirit of the last iterations of the PACE challenge, there is an exact track and a heuristic track for each problem; each track coming with a benchmark set of 100 public instances and 100 private instances. Overall, the PACE 2025 had 71 participants from 25 teams, 13 countries, and 3 continents. In this report, we briefly describe the setup of the challenge, the selection of benchmark instances, as well as the ranking of the participating teams. We also briefly outline the approaches used in the submitted solvers.
Cite as

Mario Grobler and Sebastian Siebertz. The PACE 2025 Parameterized Algorithms and Computational Experiments Challenge: Dominating Set and Hitting Set. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grobler_et_al:LIPIcs.IPEC.2025.32,
  author =	{Grobler, Mario and Siebertz, Sebastian},
  title =	{{The PACE 2025 Parameterized Algorithms and Computational Experiments Challenge: Dominating Set and Hitting Set}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{32:1--32:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.32},
  URN =		{urn:nbn:de:0030-drops-251644},
  doi =		{10.4230/LIPIcs.IPEC.2025.32},
  annote =	{Keywords: PACE 2025 Report, Dominating Set, Hitting Set, Algorithm Engineering, FPT, Heuristics}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2020.37
The PACE 2020 Parameterized Algorithms and Computational Experiments Challenge: Treedepth

Authors: Łukasz Kowalik, Marcin Mucha, Wojciech Nadara, Marcin Pilipczuk, Manuel Sorge, and Piotr Wygocki

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Abstract
This year’s Parameterized Algorithms and Computational Experiments challenge (PACE 2020) was devoted to the problem of computing the treedepth of a given graph. Altogether 51 participants from 20 teams, 12 countries and 3 continents submitted their implementations to the competition. In this report, we describe the setup of the challenge, the selection of benchmark instances and the ranking of the participating teams. We also briefly discuss the approaches used in the submitted solvers and the differences in their performance on our benchmark dataset.
Cite as

Łukasz Kowalik, Marcin Mucha, Wojciech Nadara, Marcin Pilipczuk, Manuel Sorge, and Piotr Wygocki. The PACE 2020 Parameterized Algorithms and Computational Experiments Challenge: Treedepth. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kowalik_et_al:LIPIcs.IPEC.2020.37,
  author =	{Kowalik, {\L}ukasz and Mucha, Marcin and Nadara, Wojciech and Pilipczuk, Marcin and Sorge, Manuel and Wygocki, Piotr},
  title =	{{The PACE 2020 Parameterized Algorithms and Computational Experiments Challenge: Treedepth}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{37:1--37:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.37},
  URN =		{urn:nbn:de:0030-drops-133404},
  doi =		{10.4230/LIPIcs.IPEC.2020.37},
  annote =	{Keywords: computing treedepth, contest, implementation challenge, FPT}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.63
Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}}

Authors: Piotr Sankowski and Piotr Wygocki

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
In this paper, we report progress on answering the open problem presented by Pagh [11], who considered the near neighbor search without false negatives for the Hamming distance. We show new data structures for solving the c-approximate near neighbors problem without false negatives for Euclidean high dimensional space \mathcal{R}^d. These data structures work for any c = \omega(\sqrt{\log{\log{n}}}), where n is the number of points in the input set, with poly-logarithmic query time and polynomial pre-processing time. This improves over the known algorithms, which require c to be \Omega(\sqrt{d}). This improvement is obtained by applying a sequence of reductions, which are interesting on their own. First, we reduce the problem to d instances of dimension logarithmic in n. Next, these instances are reduced to a number of c-approximate near neighbor search without false negatives instances in \big(\Rspace^k\big)^L space equipped with metric m(x,y) = \max_{1 \le i \leL}(\dist{x_i - y_i}_2).
Cite as

Piotr Sankowski and Piotr Wygocki. Approximate Nearest Neighbors Search Without False Negatives For l_2 For c>sqrt{loglog{n}}. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 63:1-63:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{sankowski_et_al:LIPIcs.ISAAC.2017.63,
  author =	{Sankowski, Piotr and Wygocki, Piotr},
  title =	{{Approximate Nearest Neighbors Search Without False Negatives For l\underline2 For c\ranglesqrt\{loglog\{n\}\}}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{63:1--63:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.63},
  URN =		{urn:nbn:de:0030-drops-82189},
  doi =		{10.4230/LIPIcs.ISAAC.2017.63},
  annote =	{Keywords: locality sensitive hashing, approximate near neighbor search, high- dimensional, similarity search}
}
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