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55,281
Fixedparameter tractability and completeness
, 1992
"... For many fixedparameter problems that are trivially solvable in polynomialtime, such as kDominating Set, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as kFeedback Vertex Set, exhibit fixedparameter tractability: for eac ..."
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Cited by 53 (6 self)
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For many fixedparameter problems that are trivially solvable in polynomialtime, such as kDominating Set, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as kFeedback Vertex Set, exhibit fixedparameter tractability
Fixedparameter tractability and logic
 IN PREPARATION
, 1999
"... We exhibit a close connection between parameterized complexity theory and logic. Our approach is that of descriptive complexity theory. We study the definability of parameterized problems and try to obtain information about the parameterized complexity of the problems through the syntactical structu ..."
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Cited by 3 (2 self)
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structure of the defining sentences. On the one hand, we use this approach to prove that certain problems are fixedparameter tractable because they can be defined by syntactically simple formulas. On the other hand, we characterize classes of intractable problems by syntactical means.
Bounded FixedParameter Tractability and Reducibility
, 2007
"... We study a refined framework of parameterized complexity theory where the parameter dependence of fixedparameter tractable algorithms is not arbitrary, but restricted by a function in some family F. For every family F of functions, this yields a notion of Ffixed parameter tractability. If F is the ..."
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Cited by 1 (1 self)
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We study a refined framework of parameterized complexity theory where the parameter dependence of fixedparameter tractable algorithms is not arbitrary, but restricted by a function in some family F. For every family F of functions, this yields a notion of Ffixed parameter tractability. If F
Imbalance is Fixed Parameter Tractable
"... Abstract. In the Imbalance Minimization problem we are given a graph G = (V, E) and an integer b and asked whether there is an ordering v1... vn of V such that the sum of the imbalance of all the vertices is at most b. The imbalance of a vertex vi is the absolute value of the difference between the ..."
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Cited by 1 (1 self)
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the number of neighbors to the left and right of vi. The problem is also known as the Balanced Vertex Ordering problem and it finds many applications in graph drawing. We show that this problem is fixed parameter tractable and provide an algorithm that runs in time 2 O(b log b) · n O(1). This resolves
Interval Deletion is FixedParameter Tractable
, 2014
"... We study the minimum interval deletion problem, which asks for the removal of a set of at most k vertices to make a graph on n vertices into an interval graph. We present a parameterized algorithm of runtime 10k · nO(1) for this problem, thereby showing its fixedparameter tractability. ..."
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Cited by 8 (4 self)
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We study the minimum interval deletion problem, which asks for the removal of a set of at most k vertices to make a graph on n vertices into an interval graph. We present a parameterized algorithm of runtime 10k · nO(1) for this problem, thereby showing its fixedparameter tractability.
Distortion is Fixed Parameter Tractable
"... We study lowdistortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective. Let M = M(G) be the shortest path metric of an edge weighted graph G, with the vertex set V (G) and the edge set E(G), on n v ..."
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Cited by 3 (2 self)
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vertices. We give the first fixed parameter tractable algorithm that for an unweighted graph metric M and integer d either constructs an embedding of M into the line with distortion at most d, or concludes that no such embedding exists. Our algorithm requires O(nd 4 (2d + 1) 2d) time which is a significant
Rotation Distance is FixedParameter Tractable
, 2009
"... Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomialtime algorithms for computing rotation distance. In the case of ordered rooted trees, we show that the rotation distance between two ordered trees is fi ..."
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Cited by 1 (0 self)
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is fixedparameter tractable, in the parameter, k, the rotation distance. The proof relies on the kernalization of the initial trees to trees with size bounded by 7k. 1
Chordal deletion is fixedparameter tractable
 In 32nd International Workshop on GraphTheoretic Concepts in Computer Science, WG 2006, LNCS Proceedings
, 2004
"... Abstract. It is known to be NPhard to decide whether a graph can be made chordal by the deletion of k vertices. Here we present a uniformly polynomialtime algorithm for the problem: the running time is f(k) ·n α for some constant α not depending on k and some f depending only on k. For large value ..."
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Cited by 35 (4 self)
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values of n, such an algorithm is much better than trying all the O(n k) possibilities. Therefore, the chordal deletion problem parameterized by the number k of vertices to be deleted is fixedparameter tractable. This answers an open question of Cai [2]. 1
FixedParameter Tractable Reductions to SAT FixedParameter Tractable Reductions to SAT
"... Abstract. Today's SAT solvers have an enormous importance and impact in many practical settings. They are used as efficient backend to solve many NPcomplete problems. However, many computational problems are located at the second level of the Polynomial Hierarchy or even higher, and hence po ..."
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polynomialtime transformations to SAT are not possible, unless the hierarchy collapses. In certain cases one can break through these complexity barriers by fixedparameter tractable (fpt) reductions which exploit structural aspects of problem instances in terms of problem parameters. Recent research
Chordal editing is fixedparameter tractable
 In 31st International Symposium on Theoretical Aspects of Computer Science
, 2014
"... Graph modification problems are typically asked as follows: is there a set of k operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and edge addition; for the same property, one can define significantly ..."
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Cited by 2 (1 self)
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edge deletions, and k3 edge additions. Clearly, this problem generalizes both chordal vertex/edge deletion and chordal completion (also known as minimum fillin). Our main result is an algorithm for chordal editing in time 2O(k log k) · nO(1), where k: = k1 + k2 + k3; therefore, the problem is fixedparameter
Results 1  10
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55,281