An FPT Algorithm and a Polynomial Kernel for Linear Rankwidth-1 Vertex Deletion
Paul, Christophe; Kim, Eun Jung; Kanté, Mamadou Moustapha; Kwon, O-joung (2015), An FPT Algorithm and a Polynomial Kernel for Linear Rankwidth-1 Vertex Deletion, IPEC: International symposium on Parameterized and Exact Computation, Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, p. 139-150. 10.4230/LIPIcs.IPEC.2015.138
TypeCommunication / Conférence
External document linkhttps://hal-lirmm.ccsd.cnrs.fr/lirmm-01264011
Conference title10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Book titleIPEC: International symposium on Parameterized and Exact Computation
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Kim, Eun Jung
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Kanté, Mamadou Moustapha
Abstract (EN)Linear rankwidth is a linearized variant of rankwidth, introduced by Oum and Seymour [Approxi-mating clique-width and branch-width. J. Combin. Theory Ser. B, 96(4):514-528, 2006.], and it is similar to pathwidth, which is the linearized variant of treewidth. Motivated from the results on graph modification problems into graphs of bounded treewidth or pathwidth, we investigate a graph modification problem into the class of graphs having linear rankwidth at most one, called the Linear Rankwidth-1 Vertex Deletion (shortly, LRW1-Vertex Deletion). In this problem, given an n-vertex graph G and a positive integer k, we want to decide whether there is a set of at most k vertices whose removal turns G into a graph of linear rankwidth at most one and if one exists, find such a vertex set. While the meta-theorem of Courcelle, Makowsky, and Rotics implies that LRW1-Vertex Deletion can be solved in time f (k) · n 3 for some function f , it is not clear whether this problem allows a runtime with a modest exponential function. We establish that LRW1-Vertex Deletion can be solved in time 8 k · n O(1). The major obstacle to this end is how to handle a long induced cycle as an obstruction. To fix this issue, we define the necklace graphs and investigate their structural properties. We also show that the LRW1-Vertex Deletion has a polynomial kernel.
Subjects / Keywords(linear) rankwidth; Distance-hereditary graphs; Thread graphs; Parameterized complexity; Kernelization
Showing items related by title and author.
Kanté, Mamadou Moustapha; Kim, Eun Jung; Kwon, O-joung; Paul, Christophe (2017) Article accepté pour publication ou publié
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