8 Search Results for "Łącki, Jakub"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.6
Optimal Decremental Connectivity in Non-Sparse Graphs

Authors: Anders Aamand, Adam Karczmarz, Jakub Łącki, Nikos Parotsidis, Peter M. R. Rasmussen, and Mikkel Thorup

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We present a dynamic algorithm for maintaining the connected and 2-edge-connected components in an undirected graph subject to edge deletions. The algorithm is Monte-Carlo randomized and processes any sequence of edge deletions in O(m + n poly log n) total time. Interspersed with the deletions, it can answer queries whether any two given vertices currently belong to the same (2-edge-)connected component in constant time. Our result is based on a general Monte-Carlo randomized reduction from decremental c-edge-connectivity to a variant of fully-dynamic c-edge-connectivity on a sparse graph. For non-sparse graphs with Ω(n poly log n) edges, our connectivity and 2-edge-connectivity algorithms handle all deletions in optimal linear total time, using existing algorithms for the respective fully-dynamic problems. This improves upon an O(m log (n² / m) + n poly log n)-time algorithm of Thorup [J.Alg. 1999], which runs in linear time only for graphs with Ω(n²) edges. Our constant amortized cost for edge deletions in decremental connectivity in non-sparse graphs should be contrasted with an Ω(log n/log log n) worst-case time lower bound in the decremental setting [Alstrup, Husfeldt, and Rauhe FOCS'98] as well as an Ω(log n) amortized time lower-bound in the fully-dynamic setting [Patrascu and Demaine STOC'04].
Cite as

Anders Aamand, Adam Karczmarz, Jakub Łącki, Nikos Parotsidis, Peter M. R. Rasmussen, and Mikkel Thorup. Optimal Decremental Connectivity in Non-Sparse Graphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 6:1-6:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{aamand_et_al:LIPIcs.ICALP.2023.6,
  author =	{Aamand, Anders and Karczmarz, Adam and {\L}\k{a}cki, Jakub and Parotsidis, Nikos and Rasmussen, Peter M. R. and Thorup, Mikkel},
  title =	{{Optimal Decremental Connectivity in Non-Sparse Graphs}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.6},
  URN =		{urn:nbn:de:0030-drops-180581},
  doi =		{10.4230/LIPIcs.ICALP.2023.6},
  annote =	{Keywords: decremental connectivity, dynamic connectivity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.86
Near-Optimal Decremental Hopsets with Applications

Authors: Jakub Łącki and Yasamin Nazari

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Given a weighted undirected graph G = (V,E,w), a hopset H of hopbound β and stretch (1+ε) is a set of edges such that for any pair of nodes u, v ∈ V, there is a path in G ∪ H of at most β hops, whose length is within a (1+ε) factor from the distance between u and v in G. We show the first efficient decremental algorithm for maintaining hopsets with a polylogarithmic hopbound. The update time of our algorithm matches the best known static algorithm up to polylogarithmic factors. All the previous decremental hopset constructions had a superpolylogarithmic (but subpolynomial) hopbound of 2^{log^{Ω(1)} n} [Bernstein, FOCS'09; HKN, FOCS'14; Chechik, FOCS'18]. By applying our decremental hopset construction, we get improved or near optimal bounds for several distance problems. Most importantly, we show how to decrementally maintain (2k-1)(1+ε)-approximate all-pairs shortest paths (for any constant k ≥ 2), in Õ(n^{1/k}) amortized update time and O(k) query time. This improves (by a polynomial factor) over the update-time of the best previously known decremental algorithm in the constant query time regime. Moreover, it improves over the result of [Chechik, FOCS'18] that has a query time of O(log log(nW)), where W is the aspect ratio, and the amortized update time is n^{1/k}⋅(1/ε)^{Õ(√{log n})}). For sparse graphs our construction nearly matches the best known static running time / query time tradeoff. We also obtain near-optimal bounds for maintaining approximate multi-source shortest paths and distance sketches, and get improved bounds for approximate single-source shortest paths. Our algorithms are randomized and our bounds hold with high probability against an oblivious adversary.
Cite as

Jakub Łącki and Yasamin Nazari. Near-Optimal Decremental Hopsets with Applications. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 86:1-86:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lacki_et_al:LIPIcs.ICALP.2022.86,
  author =	{{\L}\k{a}cki, Jakub and Nazari, Yasamin},
  title =	{{Near-Optimal Decremental Hopsets with Applications}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{86:1--86:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.86},
  URN =		{urn:nbn:de:0030-drops-164277},
  doi =		{10.4230/LIPIcs.ICALP.2022.86},
  annote =	{Keywords: Dynamic Algorithms, Data Structures, Shortest Paths, Hopsets}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.42
Good r-Divisions Imply Optimal Amortized Decremental Biconnectivity

Authors: Jacob Holm and Eva Rotenberg

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
We present a data structure that, given a graph G of n vertices and m edges, and a suitable pair of nested r-divisions of G, preprocesses G in O(m+n) time and handles any series of edge-deletions in O(m) total time while answering queries to pairwise biconnectivity in worst-case O(1) time. In case the vertices are not biconnected, the data structure can return a cutvertex separating them in worst-case O(1) time. As an immediate consequence, this gives optimal amortized decremental biconnectivity, 2-edge connectivity, and connectivity for large classes of graphs, including planar graphs and other minor free graphs.
Cite as

Jacob Holm and Eva Rotenberg. Good r-Divisions Imply Optimal Amortized Decremental Biconnectivity. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 42:1-42:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{holm_et_al:LIPIcs.STACS.2021.42,
  author =	{Holm, Jacob and Rotenberg, Eva},
  title =	{{Good r-Divisions Imply Optimal Amortized Decremental Biconnectivity}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{42:1--42:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.42},
  URN =		{urn:nbn:de:0030-drops-136875},
  doi =		{10.4230/LIPIcs.STACS.2021.42},
  annote =	{Keywords: Dynamic graphs, 2-connectivity, graph minors, r-divisions, graph separators}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.65
Reliable Hubs for Partially-Dynamic All-Pairs Shortest Paths in Directed Graphs

Authors: Adam Karczmarz and Jakub Łącki

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that handles updates in O~(mn^(4/3) log{W}/epsilon) total time (where the edge weights are from [1,W]) and explicitly maintains a (1+epsilon)-approximate distance matrix. For a fixed epsilon>0, this is the first deterministic partially dynamic algorithm for all-pairs shortest paths in directed graphs, whose update time is o(n^2) regardless of the number of edges. Furthermore, we also show how to improve the state-of-the-art partially dynamic randomized algorithms for all-pairs shortest paths [Baswana et al. STOC’02, Bernstein STOC’13] from Monte Carlo randomized to Las Vegas randomized without increasing the running time bounds (with respect to the O~(*) notation). Our results are obtained by giving new algorithms for the problem of dynamically maintaining hubs, that is a set of O~(n/d) vertices which hit a shortest path between each pair of vertices, provided it has hop-length Omega(d). We give new subquadratic deterministic and Las Vegas algorithms for maintenance of hubs under either edge insertions or deletions.
Cite as

Adam Karczmarz and Jakub Łącki. Reliable Hubs for Partially-Dynamic All-Pairs Shortest Paths in Directed Graphs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 65:1-65:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{karczmarz_et_al:LIPIcs.ESA.2019.65,
  author =	{Karczmarz, Adam and {\L}\k{a}cki, Jakub},
  title =	{{Reliable Hubs for Partially-Dynamic All-Pairs Shortest Paths in Directed Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{65:1--65:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.65},
  URN =		{urn:nbn:de:0030-drops-111862},
  doi =		{10.4230/LIPIcs.ESA.2019.65},
  annote =	{Keywords: shortest paths, dynamic, incremental, decremental, directed graphs, hubs}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.136
Stochastic Graph Exploration

Authors: Aris Anagnostopoulos, Ilan R. Cohen, Stefano Leonardi, and Jakub Łącki

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
Exploring large-scale networks is a time consuming and expensive task which is usually operated in a complex and uncertain environment. A crucial aspect of network exploration is the development of suitable strategies that decide which nodes and edges to probe at each stage of the process. To model this process, we introduce the stochastic graph exploration problem. The input is an undirected graph G=(V,E) with a source vertex s, stochastic edge costs drawn from a distribution pi_e, e in E, and rewards on vertices of maximum value R. The goal is to find a set F of edges of total cost at most B such that the subgraph of G induced by F is connected, contains s, and maximizes the total reward. This problem generalizes the stochastic knapsack problem and other stochastic probing problems recently studied. Our focus is on the development of efficient nonadaptive strategies that are competitive against the optimal adaptive strategy. A major challenge is the fact that the problem has an Omega(n) adaptivity gap even on a tree of n vertices. This is in sharp contrast with O(1) adaptivity gap of the stochastic knapsack problem, which is a special case of our problem. We circumvent this negative result by showing that O(log nR) resource augmentation suffices to obtain O(1) approximation on trees and O(log nR) approximation on general graphs. To achieve this result, we reduce stochastic graph exploration to a memoryless process - the minesweeper problem - which assigns to every edge a probability that the process terminates when the edge is probed. For this problem, interesting in its own, we present an optimal polynomial time algorithm on trees and an O(log nR) approximation for general graphs. We study also the problem in which the maximum cost of an edge is a logarithmic fraction of the budget. We show that under this condition, there exist polynomial-time oblivious strategies that use 1+epsilon budget, whose adaptivity gaps on trees and general graphs are 1+epsilon and 8+epsilon, respectively. Finally, we provide additional results on the structure and the complexity of nonadaptive and adaptive strategies.
Cite as

Aris Anagnostopoulos, Ilan R. Cohen, Stefano Leonardi, and Jakub Łącki. Stochastic Graph Exploration. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 136:1-136:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{anagnostopoulos_et_al:LIPIcs.ICALP.2019.136,
  author =	{Anagnostopoulos, Aris and Cohen, Ilan R. and Leonardi, Stefano and {\L}\k{a}cki, Jakub},
  title =	{{Stochastic Graph Exploration}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{136:1--136:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.136},
  URN =		{urn:nbn:de:0030-drops-107122},
  doi =		{10.4230/LIPIcs.ICALP.2019.136},
  annote =	{Keywords: stochastic optimization, graph exploration, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.46
Decremental SPQR-trees for Planar Graphs

Authors: Jacob Holm, Giuseppe F. Italiano, Adam Karczmarz, Jakub Lacki, and Eva Rotenberg

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
We present a decremental data structure for maintaining the SPQR-tree of a planar graph subject to edge contractions and deletions. The update time, amortized over Omega(n) operations, is O(log^2 n). Via SPQR-trees, we give a decremental data structure for maintaining 3-vertex connectivity in planar graphs. It answers queries in O(1) time and processes edge deletions and contractions in O(log^2 n) amortized time. The previous best supported deletions and insertions in O(sqrt{n}) time.
Cite as

Jacob Holm, Giuseppe F. Italiano, Adam Karczmarz, Jakub Lacki, and Eva Rotenberg. Decremental SPQR-trees for Planar Graphs. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 46:1-46:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{holm_et_al:LIPIcs.ESA.2018.46,
  author =	{Holm, Jacob and Italiano, Giuseppe F. and Karczmarz, Adam and Lacki, Jakub and Rotenberg, Eva},
  title =	{{Decremental SPQR-trees for Planar Graphs}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{46:1--46:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah 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.2018.46},
  URN =		{urn:nbn:de:0030-drops-95091},
  doi =		{10.4230/LIPIcs.ESA.2018.46},
  annote =	{Keywords: Graph embeddings, data structures, graph algorithms, planar graphs, SPQR-trees, triconnectivity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.50
Contracting a Planar Graph Efficiently

Authors: Jacob Holm, Giuseppe F. Italiano, Adam Karczmarz, Jakub Lacki, Eva Rotenberg, and Piotr Sankowski

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in O(1) time. Moreover, it can report all the arising self-loops and parallel edges. By applying the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar graph problems, including decremental 2-vertex and 3-edge connectivity, and we show that using our data structure in a black-box manner, one obtains conceptually simple optimal algorithms for computing MST and 5-coloring in planar graphs.
Cite as

Jacob Holm, Giuseppe F. Italiano, Adam Karczmarz, Jakub Lacki, Eva Rotenberg, and Piotr Sankowski. Contracting a Planar Graph Efficiently. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 50:1-50:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{holm_et_al:LIPIcs.ESA.2017.50,
  author =	{Holm, Jacob and Italiano, Giuseppe F. and Karczmarz, Adam and Lacki, Jakub and Rotenberg, Eva and Sankowski, Piotr},
  title =	{{Contracting a Planar Graph Efficiently}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.50},
  URN =		{urn:nbn:de:0030-drops-78755},
  doi =		{10.4230/LIPIcs.ESA.2017.50},
  annote =	{Keywords: planar graphs, algorithms, data structures, connectivity, coloring}
}
Document
DOI: 10.4230/LIPIcs.STACS.2015.608
Optimal Decremental Connectivity in Planar Graphs

Authors: Jakub Lacki and Piotr Sankowski

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

Abstract
We show an algorithm for dynamic maintenance of connectivity information in an undirected planar graph subject to edge deletions. Our algorithm may answer connectivity queries of the form 'Are vertices u and v connected with a path?' in constant time. The queries can be intermixed with any sequence of edge deletions, and the algorithm handles all updates in O(n) time. This results improves over previously known O(n \log n) time algorithm.
Cite as

Jakub Lacki and Piotr Sankowski. Optimal Decremental Connectivity in Planar Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 608-621, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)

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@InProceedings{lacki_et_al:LIPIcs.STACS.2015.608,
  author =	{Lacki, Jakub and Sankowski, Piotr},
  title =	{{Optimal Decremental Connectivity in Planar Graphs}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{608--621},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.608},
  URN =		{urn:nbn:de:0030-drops-49457},
  doi =		{10.4230/LIPIcs.STACS.2015.608},
  annote =	{Keywords: decremental connectivity, planar graphs, dynamic connectivity, algorithms}
}
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