2 Search Results for "Mayer, Petr"

Document
DOI: 10.4230/LIPIcs.MFCS.2024.24
Breaking a Graph into Connected Components with Small Dominating Sets

Authors: Matthias Bentert, Michael R. Fellows, Petr A. Golovach, Frances A. Rosamond, and Saket Saurabh

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We study DOMINATED CLUSTER DELETION. Therein, we are given an undirected graph G = (V,E) and integers k and d and the task is to find a set of at most k vertices such that removing these vertices results in a graph in which each connected component has a dominating set of size at most d. We also consider the special case where d is a constant. We show an almost complete tetrachotomy in terms of para-NP-hardness, containment in XP, containment in FPT, and admitting a polynomial kernel with respect to parameterizations that are a combination of k,d,c, and Δ, where c and Δ are the degeneracy and the maximum degree of the input graph, respectively. As a main contribution, we show that the problem can be solved in f(k,d) ⋅ n^O(d) time, that is, the problem is FPT when parameterized by k when d is a constant. This answers an open problem asked in a recent Dagstuhl seminar (23331). For the special case d = 1, we provide an algorithm with running time 2^𝒪(klog k) nm. Furthermore, we show that even for d = 1, the problem does not admit a polynomial kernel with respect to k + c.
Cite as

Matthias Bentert, Michael R. Fellows, Petr A. Golovach, Frances A. Rosamond, and Saket Saurabh. Breaking a Graph into Connected Components with Small Dominating Sets. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{bentert_et_al:LIPIcs.MFCS.2024.24,
  author =	{Bentert, Matthias and Fellows, Michael R. and Golovach, Petr A. and Rosamond, Frances A. and Saurabh, Saket},
  title =	{{Breaking a Graph into Connected Components with Small Dominating Sets}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.24},
  URN =		{urn:nbn:de:0030-drops-205801},
  doi =		{10.4230/LIPIcs.MFCS.2024.24},
  annote =	{Keywords: Parameterized Algorithms, Recursive Understanding, Polynomial Kernels, Degeneracy}
}
Document
DOI: 10.4230/DagSemProc.07071.7
Convergence of iterative aggregation/disaggregation methods based on splittings with cyclic iteration matrices

Authors: Ivo Marek, Ivana Pultarová, and Petr Mayer

Published in: Dagstuhl Seminar Proceedings, Volume 7071, Web Information Retrieval and Linear Algebra Algorithms (2007)

Abstract
Iterative aggregation/disaggregation methods (IAD) belong to competitive tools for computation the characteristics of Markov chains as shown in some publications devoted to testing and comparing various methods designed to this purpose. According to Dayar T., Stewart W.J., ``Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains,'' SIAM J. Sci. Comput., Vol.21, No. 5, 1691-1705 (2000), the IAD methods are effective in particular when applied to large ill posed problems. One of the purposes of this paper is to contribute to a possible explanation of this fact. The novelty may consist of the fact that the IAD algorithms do converge independently of whether the iteration matrix of the corresponding process is primitive or not. Some numerical tests are presented and possible applications mentioned; e.g. computing the PageRank.
Cite as

Ivo Marek, Ivana Pultarová, and Petr Mayer. Convergence of iterative aggregation/disaggregation methods based on splittings with cyclic iteration matrices. In Web Information Retrieval and Linear Algebra Algorithms. Dagstuhl Seminar Proceedings, Volume 7071, pp. 1-27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

Copy BibTex To Clipboard

@InProceedings{marek_et_al:DagSemProc.07071.7,
  author =	{Marek, Ivo and Pultarov\'{a}, Ivana and Mayer, Petr},
  title =	{{Convergence of iterative aggregation/disaggregation methods based on splittings with cyclic iteration matrices}},
  booktitle =	{Web Information Retrieval and Linear Algebra Algorithms},
  pages =	{1--27},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7071},
  editor =	{Andreas Frommer and Michael W. Mahoney and Daniel B. Szyld},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07071.7},
  URN =		{urn:nbn:de:0030-drops-10679},
  doi =		{10.4230/DagSemProc.07071.7},
  annote =	{Keywords: Iterative aggregation methods, stochastic matrix, stationary probability vector, Markov chains, cyclic iteration matrix, Google matrix, PageRank.}
}
  • Refine by Author
  • 1 Bentert, Matthias
  • 1 Fellows, Michael R.
  • 1 Golovach, Petr A.
  • 1 Marek, Ivo
  • 1 Mayer, Petr
  • Show More...

  • Refine by Classification
  • 1 Mathematics of computing → Graph algorithms
  • 1 Theory of computation → Parameterized complexity and exact algorithms

  • Refine by Keyword
  • 1 Degeneracy
  • 1 Google matrix
  • 1 Iterative aggregation methods
  • 1 Markov chains
  • 1 PageRank.
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2007
  • 1 2024

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact