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Parameterized complexity

Index Parameterized complexity

In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output. [1]

19 relations: Circuit satisfiability problem, Clique (graph theory), Computational complexity theory, Computational problem, Computer science, Dominating set, Function (mathematics), Graph coloring, Independent set (graph theory), Kernelization, NP-completeness, NP-hardness, P versus NP problem, Parameterized complexity, Polynomial-time approximation scheme, Reduction (complexity), Satisfiability, Time complexity, Vertex cover.

Circuit satisfiability problem

In theoretical computer science, the circuit satisfiability problem (also known as CIRCUIT-SAT, CircuitSAT, CSAT, etc.) is the decision problem of determining whether a given Boolean circuit has an assignment of its inputs that makes the output true.

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Clique (graph theory)

In the mathematical area of graph theory, a clique is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete.

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Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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Computational problem

In theoretical computer science, a computational problem is a mathematical object representing a collection of questions that computers might be able to solve.

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Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

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Dominating set

In graph theory, a dominating set for a graph G.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Graph coloring

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.

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Independent set (graph theory)

In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent.

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Kernelization

In computer science, a kernelization is a technique for designing efficient algorithms that achieve their efficiency by a preprocessing stage in which inputs to the algorithm are replaced by a smaller input, called a "kernel".

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NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

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NP-hardness

NP-hardness (''n''on-deterministic ''p''olynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP".

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P versus NP problem

The P versus NP problem is a major unsolved problem in computer science.

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Parameterized complexity

In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output.

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Polynomial-time approximation scheme

In computer science, a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems).

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Reduction (complexity)

In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem.

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Satisfiability

In mathematical logic, satisfiability and validity are elementary concepts of semantics.

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Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

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Vertex cover

In the mathematical discipline of graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set.

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Redirects here:

FPT (complexity class), Fixed-parameter algorithm, Fixed-parameter tractability, Fixed-parameter tractable, Parameterised complexity, Parameterized (Multivariate) Complexity, Parameterized Complexity, Parametrised complexity, Parametrized complexity, W (complexity class), W Hierarchy, W hierarchy, W(1), W(2), W-Hierarchy, W-hierarchy, XP (class), XP (complexity class).

References

[1] https://en.wikipedia.org/wiki/Parameterized_complexity

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