# Questions tagged [fixed-parameter-tractable]

algorithms for parameterized problems where the run-time is polynomial in the input size, but depends arbitrarily on the parameter

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### On Random Self-reducible properties

Permanent is random self-reducible. $\mathsf{SAT}$ is not random self-reducible since otherwise the polynomial hierarchy collapses to $\mathsf{\Sigma_3}$. 1) Is $k$-sum random self-reducible? That ...
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### Exact Algorithms for r-Dominating Set on Bounded Treewidth Graphs

Given a graph, $G = (V, E)$, I want to find an optimal $r$-domination for $G$. That is, I want a subset $S$ of $V$ such that all vertices in $G$ are at a distance of at most $r$ from some vertex in $S$...
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### Books/Lecture Notes on Parametrized Complexity

I would like to learn about Parametrized Complexity (both on the algorithmic side and on the hardness side). What books/lecture notes can I read on this subject?
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### What is the motivation behind the definition of fixed parameter tractability?

Wikipedia writes: FPT contains the fixed parameter tractable problems, which are those that can be solved in time $f(k)\cdot|x|^{O(1)}$ for some computable function $f$. Typically, this ...
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### Algebraic formulation for packing problem

My question is regarding the algebraic formulation for packing problems in graphs. Taking an example, suppose I am interested in the problem of finding if there is a packing of k edge disjoint ...
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### Complement problems are not in the same class in parametrized complexity hierarchy? If not in $P$

By "complement problems", I mean the two problems' objective functions are complement. For example, the vertex cover and its complement independent set in this sense. For a graph $G(V,E)$, their ...
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### Variants of Cluster-Vertex-Deletion problem

The Unweighted Cluster-Vertex-Deletion problem is the following: Input: An undirected graph G = (V, E) and a nonnegative number k Output: Is there a subset X ⊆ V with |X| ≤ k such that deleting all ...
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### Elementary bounds on parameter in fixed-parameter tractability?

In the definition of (strong) fixed-parameter tractability, the time bound is an expression of the form $$f(k).p(|x|),$$ where the input instance is $(x,k)$ with parameter $k$, $p$ is a polynomial, ...