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Fast FixedParameter Tractable Algorithms for Nontrivial Generalizations of Vertex Cover
, 2003
"... Our 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 ..."
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Cited by 15 (0 self)
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Our 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 ist the class of edgeless graphs,...
Contributions to Parameterized Complexity
, 2003
"... This thesis is presented in two parts. In Part One we concentrate on algorithmic aspects of parameterized complexity. We explore ways in which the concepts and algorithmic techniques of parameterized complexity can be fruitfully brought to bear on a (classically) wellstudied problem area, that of s ..."
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Cited by 4 (3 self)
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This thesis is presented in two parts. In Part One we concentrate on algorithmic aspects of parameterized complexity. We explore ways in which the concepts and algorithmic techniques of parameterized complexity can be fruitfully brought to bear on a (classically) wellstudied problem area, that of scheduling problems modelled on partial orderings. We develop efficient and constructive algorithms for parameterized versions of some classically intractable scheduling problems.
A Simple LinearTime Algorithm for Finding PathDecompositions of Small Width
 also University of Victoria manuscript
, 1996
"... We described a simple algorithm running in linear time for each fixed constant k, that either establishes that the pathwidth of a graph G is greater than k, or finds a pathdecomposition of G of width at most O(2^k). This provides a simple proof of the result by Bodlaender that many families of grap ..."
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Cited by 3 (2 self)
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We described a simple algorithm running in linear time for each fixed constant k, that either establishes that the pathwidth of a graph G is greater than k, or finds a pathdecomposition of G of width at most O(2^k). This provides a simple proof of the result by Bodlaender that many families of graphs of bounded pathwidth can be recognized in linear time.
Forbidden Minors to Graphs with Small Feedback Sets
 DISCRETE MATHEMATICS
, 1996
"... Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. In this paper wecharacterize several families of graphs with small feedback sets, namely k 1 Feedback Vertex Set, k 2 Feedback Edge Set and #k 1 ,k 2 ##Feedback Ver ..."
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Cited by 3 (1 self)
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Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. In this paper wecharacterize several families of graphs with small feedback sets, namely k 1 Feedback Vertex Set, k 2 Feedback Edge Set and #k 1 ,k 2 ##Feedback Vertex#Edge Set, for small integer parameters k 1 and k 2 . Our constructive methods can compute obstruction sets for any minorclosed family of graphs, provided the pathwidth #or treewidth# of the largest obstruction is known.