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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. 1
FixedParameter TRACTABILITY AND COMPLETENESS I: BASIC Results
, 1995
"... For many fixedparameter problems that are trivially soluable in polynomial time, such as (k)DOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as (k)FEEDBACK VERTEX SET, exhibit fixedparameter tractability: fo ..."
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Cited by 111 (15 self)
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For many fixedparameter problems that are trivially soluable in polynomial time, such as (k)DOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as (k)FEEDBACK VERTEX SET, exhibit fixedparameter tractability
Fixedparameter
"... tractable canonization and isomorphism test for graphs of bounded treewidth∗ ..."
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tractable canonization and isomorphism test for graphs of bounded treewidth∗
Fixedparameter
"... tractable canonization and isomorphism test for graphs of bounded treewidth∗ ..."
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tractable canonization and isomorphism test for graphs of bounded treewidth∗
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 34 (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
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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is the class of all polynomially bounded functions, then Ffixed parameter tractability coincides with polynomial time decidability and if F is the class of all computable functions, Ffixed parameter tractability coincides with the standard notion of fixedparameter tractability. There are interesting choices
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
Results 1  10
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