1 Search Results for "Tuza, Zsolt"


Document
H-Free Graphs, Independent Sets, and Subexponential-Time Algorithms

Authors: Gábor Bacsó, Dániel Marx, and Zsolt Tuza

Published in: LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)


Abstract
It is an outstanding open question in algorithmic graph theory to determine the complexity of the MAXIMUM INDEPENDENT SET problem on P_t-free graphs, that is, on graphs not containing any induced path on t vertices. So far, polynomial-time algorithms are known only for t at most 5 [Lokshtanov et al., SODA 2014, 570-581, 2014]. Here we study the existence of subexponential-time algorithms for the problem: by generalizing an earlier result of Randerath and Schiermeyer for t=5 [Discrete App. Math., 158 (2010), 1041-1044], we show that for any t at least 5, there is an algorithm for MAXIMUM INDEPENDENT SET on P_t-free graphs whose running time is subexponential in the number of vertices. SCATTERED SET is the generalization of MAXIMUM INDEPENDENT SET where the vertices of the solution are required to be at distance at least $d$ from each other. We give a complete characterization of those graphs H for which SCATTERED SET on H-free graphs can be solved in time subexponential in the size of the input (that is, in the number of vertices plus the number of edges): * If every component of H is a path, then d-SCATTERED SET on H-free graphs with n vertices and m edges can be solved in time 2^{(n+m)^{1-O(1/|V(H)|)}}, even if d is part of the input. * Otherwise, assuming ETH, there is no 2^{o(n+m)} time algorithm for d-SCATTERED SET for any fixed d at least 3 on H-free graphs with n vertices and m edges.

Cite as

Gábor Bacsó, Dániel Marx, and Zsolt Tuza. H-Free Graphs, Independent Sets, and Subexponential-Time Algorithms. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 3:1-3:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Copy BibTex To Clipboard

@InProceedings{bacso_et_al:LIPIcs.IPEC.2016.3,
  author =	{Bacs\'{o}, G\'{a}bor and Marx, D\'{a}niel and Tuza, Zsolt},
  title =	{{H-Free Graphs, Independent Sets, and Subexponential-Time Algorithms}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{3:1--3:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Guo, Jiong and Hermelin, Danny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.3},
  URN =		{urn:nbn:de:0030-drops-69397},
  doi =		{10.4230/LIPIcs.IPEC.2016.3},
  annote =	{Keywords: independent set, scattered set, subexponential algorithms, H-free graphs}
}
  • Refine by Author
  • 1 Bacsó, Gábor
  • 1 Marx, Dániel
  • 1 Tuza, Zsolt

  • Refine by Classification

  • Refine by Keyword
  • 1 H-free graphs
  • 1 independent set
  • 1 scattered set
  • 1 subexponential algorithms

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2017

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