• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

Thumbnail
Date
2016
Link to item file
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01288472
Dewey
Principes généraux des mathématiques
Sujet
Theory of computation; Design and analysis of algorithms; Parameterized complexity and exact algorithms; Fixed parameter tractability
Journal issue
ACM Transactions on Algorithms
Volume
12
Number
2
Publication date
2016
DOI
http://dx.doi.org/10.1145/2797140
URI
https://basepub.dauphine.fr/handle/123456789/20789
Collections
  • LAMSADE : Publications
Metadata
Show full item record
Author
Kim, Eun Jung
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Langer, Alexander
Paul, Christophe
Reidl, Felix
Rossmanith, Peter
Sau Valls, Ignasi
Type
Article accepté pour publication ou publié
Abstract (EN)
We present a linear-time algorithm to compute a decomposition scheme for graphs G that have a set X⊆V(G), called a treewidth-modulator, such that the treewidth of G − X is bounded by a constant. Our decomposition, called a protrusion decomposition, is the cornerstone in obtaining the following two main results. Our first result is that any parameterized graph problem (with parameter k) that has a finite integer index and such that Yes-instances have a treewidth-modulator of size O(k) admits a linear kernel on the class of H-topological-minor-free graphs, for any fixed graph H. This result partially extends previous meta-theorems on the existence of linear kernels on graphs of bounded genus and H-minor-free graphs. Let F be a fixed finite family of graphs containing at least one planar graph. Given an n-vertex graph G and a non-negative integer k, Planar-F-Deletion asks whether G has a set X⊆V(G) such that |X| ⩽ k and G − X is H-minor-free for every H ϵ F. As our second application, we present the first single-exponential algorithm to solve Planar-F-Deletion. Namely, our algorithm runs in time 2O(k) · n2, which is asymptotically optimal with respect to k. So far, single-exponential algorithms were only known for special cases of the family F.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.