Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions
Kim, Eun Jung; Langer, Alexander; Paul, Christophe; Reidl, Felix; Rossmanith, Peter; Sau Valls, Ignasi (2016), Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions, ACM Transactions on Algorithms, 12, 2. 10.1145/2797140
TypeArticle accepté pour publication ou publié
External document linkhttps://hal-lirmm.ccsd.cnrs.fr/lirmm-01288472
Journal nameACM Transactions on Algorithms
MetadataShow full item record
Author(s)Kim, Eun Jung
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Sau Valls, Ignasi
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.
Subjects / KeywordsTheory of computation; Design and analysis of algorithms; Parameterized complexity and exact algorithms; Fixed parameter tractability
Showing items related by title and author.
Kim, Eun Jung; Langer, Alexander; Paul, Christophe; Reidl, Felix; Rossmanith, Peter; Sau Valls, Ignasi; Sikdar, Somnath (2013-07) Communication / Conférence
Kim, Eun Jung; Paul, Christophe; Sau Valls, Ignasi; Thilikos, Dimitrios M. (2017) Article accepté pour publication ou publié
Cohen, Nathann; Gonçalves, Daniel; Kim, Eun Jung; Paul, Christophe; Sau Valls, Ignasi; Thilikos, Dimitrios M. (2017) Article accepté pour publication ou publié