3 Search Results for "Czygrinow, Andrzej"


Document
Distributed Approximations of f-Matchings and b-Matchings in Graphs of Sub-Logarithmic Expansion

Authors: Andrzej Czygrinow, Michał Hanćkowiak, and Marcin Witkowski

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)


Abstract
We give a distributed algorithm which given ε > 0 finds a (1-ε)-factor approximation of a maximum f-matching in graphs G = (V,E) of sub-logarithmic expansion. Using a similar approach we also give a distributed approximation of a maximum b-matching in the same class of graphs provided the function b: V → ℤ^+ is L-Lipschitz for some constant L. Both algorithms run in O(log^* n) rounds in the LOCAL model, which is optimal.

Cite as

Andrzej Czygrinow, Michał Hanćkowiak, and Marcin Witkowski. Distributed Approximations of f-Matchings and b-Matchings in Graphs of Sub-Logarithmic Expansion. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 59:1-59:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{czygrinow_et_al:LIPIcs.ISAAC.2021.59,
  author =	{Czygrinow, Andrzej and Han\'{c}kowiak, Micha{\l} and Witkowski, Marcin},
  title =	{{Distributed Approximations of f-Matchings and b-Matchings in Graphs of Sub-Logarithmic Expansion}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{59:1--59:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.59},
  URN =		{urn:nbn:de:0030-drops-154925},
  doi =		{10.4230/LIPIcs.ISAAC.2021.59},
  annote =	{Keywords: Distributed algorithms, f-matching, b-matching}
}
Document
Distributed Minimum Vertex Coloring and Maximum Independent Set in Chordal Graphs

Authors: Christian Konrad and Viktor Zamaraev

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
We give deterministic distributed (1+epsilon)-approximation algorithms for Minimum Vertex Coloring and Maximum Independent Set on chordal graphs in the LOCAL model. Our coloring algorithm runs in O( (1 / epsilon) log n) rounds, and our independent set algorithm has a runtime of O( (1/epsilon) log(1/epsilon)log^* n) rounds. For coloring, existing lower bounds imply that the dependencies on 1/epsilon and log n are best possible. For independent set, we prove that Omega(1/epsilon) rounds are necessary. Both our algorithms make use of the tree decomposition of the input chordal graph. They iteratively peel off interval subgraphs, which are identified via the tree decomposition of the input graph, thereby partitioning the vertex set into O(log n) layers. For coloring, each interval graph is colored independently, which results in various coloring conflicts between the layers. These conflicts are then resolved in a separate phase, using the particular structure of our partitioning. For independent set, only the first O(log (1/epsilon)) layers are required as they already contain a large enough independent set. We develop a (1+epsilon)-approximation maximum independent set algorithm for interval graphs, which we then apply to those layers. This work raises the question as to how useful tree decompositions are for distributed computing.

Cite as

Christian Konrad and Viktor Zamaraev. Distributed Minimum Vertex Coloring and Maximum Independent Set in Chordal Graphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{konrad_et_al:LIPIcs.MFCS.2019.21,
  author =	{Konrad, Christian and Zamaraev, Viktor},
  title =	{{Distributed Minimum Vertex Coloring and Maximum Independent Set in Chordal Graphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.21},
  URN =		{urn:nbn:de:0030-drops-109651},
  doi =		{10.4230/LIPIcs.MFCS.2019.21},
  annote =	{Keywords: local model, approximation algorithms, minimum vertex coloring, maximum independent set, chordal graphs}
}
Document
Distributed Approximation Algorithms for the Minimum Dominating Set in K_h-Minor-Free Graphs

Authors: Andrzej Czygrinow, Michal Hanckowiak, Wojciech Wawrzyniak, and Marcin Witkowski

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)


Abstract
In this paper we will give two distributed approximation algorithms (in the Local model) for the minimum dominating set problem. First we will give a distributed algorithm which finds a dominating set D of size O(gamma(G)) in a graph G which has no topological copy of K_h. The algorithm runs L_h rounds where L_h is a constant which depends on h only. This procedure can be used to obtain a distributed algorithm which given epsilon>0 finds in a graph G with no K_h-minor a dominating set D of size at most (1+epsilon)gamma(G). The second algorithm runs in O(log^*{|V(G)|}) rounds.

Cite as

Andrzej Czygrinow, Michal Hanckowiak, Wojciech Wawrzyniak, and Marcin Witkowski. Distributed Approximation Algorithms for the Minimum Dominating Set in K_h-Minor-Free Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 22:1-22:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{czygrinow_et_al:LIPIcs.ISAAC.2018.22,
  author =	{Czygrinow, Andrzej and Hanckowiak, Michal and Wawrzyniak, Wojciech and Witkowski, Marcin},
  title =	{{Distributed Approximation Algorithms for the Minimum Dominating Set in K\underlineh-Minor-Free Graphs}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{22:1--22:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.22},
  URN =		{urn:nbn:de:0030-drops-99705},
  doi =		{10.4230/LIPIcs.ISAAC.2018.22},
  annote =	{Keywords: Distributed algorithms, minor-closed family of graphs, MDS}
}
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