License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.30
URN: urn:nbn:de:0030-drops-169687
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16968/
Go to the corresponding LIPIcs Volume Portal

Bumpus, Benjamin Merlin ; Jansen, Bart M. P. ; de Kroon, Jari J. H.

Search-Space Reduction via Essential Vertices

pdf-format:
LIPIcs-ESA-2022-30.pdf (1 MB)

Abstract

We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total instance size, our focus is on finding a non-empty vertex set that belongs to an optimal solution. This decreases the size of the remaining part of the solution which still has to be found, and therefore shrinks the search space of fixed-parameter tractable algorithms for parameterizations based on the solution size. We introduce the notion of a c-essential vertex as one that is contained in all c-approximate solutions. For several classic combinatorial problems such as Odd Cycle Transversal and Directed Feedback Vertex Set, we show that under mild conditions a polynomial-time preprocessing algorithm can find a subset of an optimal solution that contains all 2-essential vertices, by exploiting packing/covering duality. This leads to FPT algorithms to solve these problems where the exponential term in the running time depends only on the number of non-essential vertices in the solution.

BibTeX - Entry

@InProceedings{bumpus_et_al:LIPIcs.ESA.2022.30,
  author =	{Bumpus, Benjamin Merlin and Jansen, Bart M. P. and de Kroon, Jari J. H.},
  title =	{{Search-Space Reduction via Essential Vertices}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{30:1--30:15},
  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/opus/volltexte/2022/16968},
  URN =		{urn:nbn:de:0030-drops-169687},
  doi =		{10.4230/LIPIcs.ESA.2022.30},
  annote =	{Keywords: fixed-parameter tractability, essential vertices, covering versus packing}
}

Keywords: fixed-parameter tractability, essential vertices, covering versus packing
Collection: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue Date: 2022
Date of publication: 01.09.2022

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI