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Documents authored by Smulewicz, Marcin

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.95
Fully Dynamic Strongly Connected Components in Planar Digraphs

Authors: Adam Karczmarz and Marcin Smulewicz

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In this paper we consider maintaining strongly connected components (SCCs) of a directed planar graph subject to edge insertions and deletions. We show a data structure maintaining an implicit representation of the SCCs within Õ(n^{6/7}) worst-case time per update. The data structure supports, in O(log²{n}) time, reporting vertices of any specified SCC (with constant overhead per reported vertex) and aggregating vertex information (e.g., computing the maximum label) over all the vertices of that SCC. Furthermore, it can maintain global information about the structure of SCCs, such as the number of SCCs, or the size of the largest SCC. To the best of our knowledge, no fully dynamic SCCs data structures with sublinear update time have been previously known for any major subclass of digraphs. Our result should be contrasted with the n^{1-o(1)} amortized update time lower bound conditional on SETH, which holds even for dynamically maintaining whether a general digraph has more than two SCCs.
Cite as

Adam Karczmarz and Marcin Smulewicz. Fully Dynamic Strongly Connected Components in Planar Digraphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 95:1-95:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{karczmarz_et_al:LIPIcs.ICALP.2024.95,
  author =	{Karczmarz, Adam and Smulewicz, Marcin},
  title =	{{Fully Dynamic Strongly Connected Components in Planar Digraphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{95:1--95:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.95},
  URN =		{urn:nbn:de:0030-drops-202388},
  doi =		{10.4230/LIPIcs.ICALP.2024.95},
  annote =	{Keywords: dynamic strongly connected components, dynamic strong connectivity, dynamic reachability, planar graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.68
On Fully Dynamic Strongly Connected Components

Authors: Adam Karczmarz and Marcin Smulewicz

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We consider maintaining strongly connected components (SCCs) of a directed graph subject to edge insertions and deletions. For this problem, we show a randomized algebraic data structure with conditionally tight O(n^1.529) worst-case update time. The only previously described subquadratic update bound for this problem [Karczmarz, Mukherjee, and Sankowski, STOC'22] holds exclusively in the amortized sense. For the less general dynamic strong connectivity problem, where one is only interested in maintaining whether the graph is strongly connected, we give an efficient deterministic black-box reduction to (arbitrary-pair) dynamic reachability. Consequently, for dynamic strong connectivity we match the best-known O(n^1.407) worst-case upper bound for dynamic reachability [van den Brand, Nanongkai, and Saranurak FOCS'19]. This is also conditionally optimal and improves upon the previous O(n^1.529) bound. Our reduction also yields the first fully dynamic algorithms for maintaining the minimum strong connectivity augmentation of a digraph.
Cite as

Adam Karczmarz and Marcin Smulewicz. On Fully Dynamic Strongly Connected Components. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 68:1-68:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{karczmarz_et_al:LIPIcs.ESA.2023.68,
  author =	{Karczmarz, Adam and Smulewicz, Marcin},
  title =	{{On Fully Dynamic Strongly Connected Components}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{68:1--68:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.68},
  URN =		{urn:nbn:de:0030-drops-187211},
  doi =		{10.4230/LIPIcs.ESA.2023.68},
  annote =	{Keywords: dynamic strongly connected components, dynamic strong connectivity, dynamic reachability}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.79
Computing Treedepth in Polynomial Space and Linear FPT Time

Authors: Wojciech Nadara, Michał Pilipczuk, and Marcin Smulewicz

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
The treedepth of a graph G is the least possible depth of an elimination forest of G: a rooted forest on the same vertex set where every pair of vertices adjacent in G is bound by the ancestor/descendant relation. We propose an algorithm that given a graph G and an integer d, either finds an elimination forest of G of depth at most d or concludes that no such forest exists; thus the algorithm decides whether the treedepth of G is at most d. The running time is 2^𝒪(d²)⋅n^𝒪(1) and the space usage is polynomial in n. Further, by allowing randomization, the time and space complexities can be improved to 2^𝒪(d²)⋅n and d^𝒪(1)⋅n, respectively. This improves upon the algorithm of Reidl et al. [ICALP 2014], which also has time complexity 2^𝒪(d²)⋅n, but uses exponential space.
Cite as

Wojciech Nadara, Michał Pilipczuk, and Marcin Smulewicz. Computing Treedepth in Polynomial Space and Linear FPT Time. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 79:1-79:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{nadara_et_al:LIPIcs.ESA.2022.79,
  author =	{Nadara, Wojciech and Pilipczuk, Micha{\l} and Smulewicz, Marcin},
  title =	{{Computing Treedepth in Polynomial Space and Linear FPT Time}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{79:1--79:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.79},
  URN =		{urn:nbn:de:0030-drops-170175},
  doi =		{10.4230/LIPIcs.ESA.2022.79},
  annote =	{Keywords: treedepth, FPT, polynomial space}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.71
Determining 4-Edge-Connected Components in Linear Time

Authors: Wojciech Nadara, Mateusz Radecki, Marcin Smulewicz, and Marek Sokołowski

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In this work, we present the first linear time deterministic algorithm computing the 4-edge-connected components of an undirected graph. First, we show an algorithm listing all 3-edge-cuts in a given 3-edge-connected graph, and then we use the output of this algorithm in order to determine the 4-edge-connected components of the graph.
Cite as

Wojciech Nadara, Mateusz Radecki, Marcin Smulewicz, and Marek Sokołowski. Determining 4-Edge-Connected Components in Linear Time. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 71:1-71:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{nadara_et_al:LIPIcs.ESA.2021.71,
  author =	{Nadara, Wojciech and Radecki, Mateusz and Smulewicz, Marcin and Soko{\l}owski, Marek},
  title =	{{Determining 4-Edge-Connected Components in Linear Time}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{71:1--71:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.71},
  URN =		{urn:nbn:de:0030-drops-146523},
  doi =		{10.4230/LIPIcs.ESA.2021.71},
  annote =	{Keywords: graphs, connectivity, cuts}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.66
Many Visits TSP Revisited

Authors: Łukasz Kowalik, Shaohua Li, Wojciech Nadara, Marcin Smulewicz, and Magnus Wahlström

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
We study the Many Visits TSP problem, where given a number k(v) for each of n cities and pairwise (possibly asymmetric) integer distances, one has to find an optimal tour that visits each city v exactly k(v) times. The currently fastest algorithm is due to Berger, Kozma, Mnich and Vincze [SODA 2019, TALG 2020] and runs in time and space O*(5ⁿ). They also show a polynomial space algorithm running in time O(16^{n+o(n)}). In this work, we show three main results: - A randomized polynomial space algorithm in time O*(2^n D), where D is the maximum distance between two cities. By using standard methods, this results in a (1+ε)-approximation in time O*(2ⁿε^{-1}). Improving the constant 2 in these results would be a major breakthrough, as it would result in improving the O*(2ⁿ)-time algorithm for Directed Hamiltonian Cycle, which is a 50 years old open problem. - A tight analysis of Berger et al.’s exponential space algorithm, resulting in an O*(4ⁿ) running time bound. - A new polynomial space algorithm, running in time O(7.88ⁿ).
Cite as

Łukasz Kowalik, Shaohua Li, Wojciech Nadara, Marcin Smulewicz, and Magnus Wahlström. Many Visits TSP Revisited. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 66:1-66:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kowalik_et_al:LIPIcs.ESA.2020.66,
  author =	{Kowalik, {\L}ukasz and Li, Shaohua and Nadara, Wojciech and Smulewicz, Marcin and Wahlstr\"{o}m, Magnus},
  title =	{{Many Visits TSP Revisited}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{66:1--66:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.66},
  URN =		{urn:nbn:de:0030-drops-129329},
  doi =		{10.4230/LIPIcs.ESA.2020.66},
  annote =	{Keywords: many visits traveling salesman problem, exponential algorithm}
}
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