Fixed parameter tractable

Ein entscheidbares Problem ist genau dann fixed parameter tractable , wenn dafür eine Problemkern-Reduktion existiert, die in Polynomialzeit berechenbar ist und die eine Instanz mit Parameter k reduziert auf eine Instanz, deren Größe durch eine Funktion f(k) beschränkt ist. Den Problemkern kann man dann mit einem . Fixed - Parameter Tractability and many queries that occur in practice are conjunctive queries. As a second example, we consider a central algorithmic problem in au- tomated verification, the problem of checking that a finite state system, . We investigate two techniques used to construct fixed paramemter algorithms: bounded search tree method . Problems in which some parameter k is fixed are called parameterized problems.

We extend this result to a meta-theorem by defining a broad class of properties of triangulations, each with a corresponding fixed parameter tractable existence algorithm. We explicitly implement this algorithm in the most generic setting, and we identify heuristics that in practice are seen to mitigate the . The running time of the algorithm on an -vertex graph is , and this is the first fixed-parameter . We consider the following problem. Given a 2-cnf formula, is it possible to remove at most k clauses so that the resulting 2-cnf formula is satisfiable? This problem is known to different research communities in theoretical computer science under the names Almost 2-SAT, All-but-k 2-SAT, 2-cnf deletion, and 2-SAT deletion. Fixed - parameter tractability of NP optimization problems is studied by relating it to approximability of the problems.

It is shown that an NP optimization problem is fixed - parameter tractable if it admits a fully polynomial-time approximation scheme, or if it belongs to the class. The Imbalance Minimization problem on graphs asks for an ordering of the vertices such that the total imbalance is minimized. The problem finds several applications in graph drawing, and is known to be NP-hard. In this article, we show that the problem is fixed parameter tractable , when parameterized by the solution . This matches (up to the base of the exponential) the best algorithms for finding a path of length . When restricted to 1-dimensional subspaces, this problem is equivalent to computing the trellis-width (or minimum trellis state-complexity) of a linear code in coding theory and computing the path-width of an F-represented matroid in matroid theory.

We give a fixed - parameter tractable algorithm that, given a parameter $k$ and two graphs $G_G_2$, either concludes that one of these graphs has treewidth at least $k$ or determines whether $G_1$ and $G_2$ are isomorphic. We present a fixed - parameter tractable algorithm to . The goal of parameterized complexity is to design efficient algorithms for NP-hard problems when the parameter k is small, even if the input size is large. Formally, we say that a parameterized problem is fixed - parameter tractable (FPT) if instances of size n and parameter k can be solved in f(k). 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 or concludes that no such embedding exists.

Ronald de Haan Martin Kronegger and Andreas Pfandlerfirstname. Planning is an important AI task that gives rise to many hard problems. Definition: A parameterization of a decision problem is a function that assigns an integer parameter k to each input instance x. University of Siegen, Germany. Example: MINIMUM VERTEX COVER . For many fixed-parameter problems that are trivially . Computer Science Department. Viele übersetzte Beispielsätze mit fixed parameter tractable – Deutsch-Englisch Wörterbuch und Suchmaschine für Millionen von Deutsch-Übersetzungen.

More precisely, let FPT be the family of the fixed parameter tractable prob- lems. Bordewich M(1), Semple C. Power is fixed - parameter tractable with respect to the parameter r. Key words: fixed - parameter tractability , graph algorithm, graph modification, graph power, leaf power, forbidden subgraph characterization. Graph powers form a classical concept in graph theory, and the rich literature dates back to the sixties . Unsurprisingly, there are classes of parameterized problems that are presumably not fixed - parameter tractable.

The first such class is, of course, the class of parameterized languages that are NP-hard even for constant parameter values. Such problems cannot be fixed - parameter tractable unless P= NP. Multiple Target Structures.

Stefan Hammer Yann Ponty⋆, Wei Wang and Sebastian Will2.