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dc.contributor.authorNishimura, Naomi
dc.contributor.authorRagde, Prabhakar
dc.contributor.authorThilikos Touloupas, Dimitrios
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Ciències de la Computació
dc.date.accessioned2016-12-07T11:54:12Z
dc.date.available2016-12-07T11:54:12Z
dc.date.issued2001-09
dc.identifier.citationNishimura, N., Ragde, P., Thilikos, D. "Fast fixed-parameter tractable algorithms for (nontrivial) generalizations of vertex cover". 2001.
dc.identifier.urihttp://hdl.handle.net/2117/97846
dc.description.abstractOur goal in this paper is the development of fast algorithms for recognizing general classes of graphs. We seek algorithms whose complexity can be expressed as a linear function of the graph size plus an exponential function of k, a natural parameter describing the class. In particular, we consider the class W_k(G), where for each graph G in W_k(G), the removal of a set of at most k vertices from G results in a graph in the base graph class G. (If G is the class of edgeless graphs, W_k(G) is the class of graphs with bounded vertex cover.) When G is a minor-closed class such that each graph in G has bounded maximum degree, and all obstructions of G (minor-minimal graphs outside G) are connected, we obtain an O((g+k)|V(G)|+(fk)^k) recognition algorithm for W_k(G), where g and f are constants (modest and quantified) depending on the class G. If G is the class of graphs with maximum degree bounded by D (not closed under minors), we can still obtain a running time of O(|V(G)|(D+k)+k(D+k)^{k+3}) for recognition of graphs in W_k(G). Our results are obtained by considering minor-closed classes for which all obstructions are connected graphs, and showing that the size of any obstruction for W_k(G) is O(tk^7+t^7k^2), where t is a bound on the size of obstructions for G. A trivial corollary of this result is an upper bound of (k+1)(k+2) on the number of vertices in any obstruction of the class of graphs with vertex cover of size at most k. These results are of independent graph-theoretic interest.
dc.format.extent20 p.
dc.language.isoeng
dc.relation.ispartofseriesLSI-01-39-R
dc.subjectÀrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica
dc.subject.otherFast algorithms
dc.subject.otherGraphs class recognition
dc.subject.otherGraphs minors
dc.subject.otherVertex covers
dc.subject.otherObstructions
dc.titleFast fixed-parameter tractable algorithms for (nontrivial) generalizations of vertex cover
dc.typeExternal research report
dc.rights.accessOpen Access
local.identifier.drac1903024
dc.description.versionPostprint (published version)
local.citation.authorNishimura, N.; Ragde, P.; Thilikos, D.


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