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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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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
DIRECTED GRAPHS: FIXEDPARAMETER TRACTABILITY & BEYOND
, 2014
"... Most interesting optimization problems on graphs are NPhard, implying that (unless P = NP) there is no polynomial time algorithm that solves all the instances of an NPhard problem exactly. However, classical complexity measures the running time as a function of only the overall input size. The pa ..."
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plexity is to design efficient algorithms for NPhard problems when the parameter k is small, even if the input size is large. Formally, we say that a parameterized problem is fixedparameter tractable (FPT) if instances of size n and parameter k can be solved in f (k) · nO(1) time, where f is a computable function
Fixedparameter algorithms for . . .
, 2003
"... FestparameterAlgorithmen bieten einen konstruktiven Ansatz zur Losung von kombinatorisch schwierigen, in der Regel NPharten Problemen, der zwei Ziele berucksichtigt: innerhalb von beweisbaren Laufzeitschranken werden optimale Ergebnisse berechnet. Die entscheidende Idee ist dabei, einen oder mehr ..."
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mehrere Aspekte der Problemeingabe als Parameter der Problems aufzufassen und die kombinatorische Explosion der algorithmischen Schwierigkeit auf diese Parameter zu beschranken, so dass die Laufzeitkosten polynomiell in Bezug auf den nichtparametrisierten Teil der Eingabe sind. Gibt es einen
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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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
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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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
Scheduling Meets FixedParameter Tractability
"... Abstract. Fixedparameter tractability analysis and scheduling are two core domains of combinatorial optimization which led to deep understanding of many important algorithmic questions. However, even though fixedparameter algorithms are appealing for many reasons, no such algorithms are known for ..."
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Abstract. Fixedparameter tractability analysis and scheduling are two core domains of combinatorial optimization which led to deep understanding of many important algorithmic questions. However, even though fixedparameter algorithms are appealing for many reasons, no such algorithms are known
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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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
Evolving Fixedparameter Tractable Algorithms
"... The following full text is a publisher's version. ..."
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