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# Questions tagged [parameterized-complexity]

Computational complexity with respect to one or more parameters of the input (apart from its plain length as a string), which capture intrinsically difficult instances

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### How to find parameter sets for a big-O expression to be fixed-parameter tractable?

I've been stuck on the following assignment taken from Cognition and Intractability: A Guide to Classical and Parameterized Complexity Analysis: Imagine that the following big-O expressions ...
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### Does FPT allow for doubling the parameter?

I have recently come across a result that showed that a given problem is in FPT when parameterized by the treewidth of a graph. However, they did this by showing that the problem is in FPT when ...
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### First-order model checking is not fixed parameter tractable on general graphs

I read that the problem of first-order model checking is believed to be not fixed parameter tractable on general graphs. Why is this the case? Would be happy about some reference Thanks in advance!
1 vote
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### First-order model checking on general graphs is intractable

I read that the first-order model checking problem is intractable on general graphs. How is this shown? Would be happy about some reference! Thanks in advance
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### most cost-effective route w.r.t. gas in a labelled graph

Consider a car that can hold gas to travel a distance of $c \in N$ kilometers (its capacity) on a full tank that's initially empty. The car starts in node $s \in V$ of a graph. Each vertex $V_i$ of ...
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### Tree Decomposition Construction with Balanced Separations: Why 2/3?

I am working through the book "Parameterized Algorithms" https://www.mimuw.edu.pl/~malcin/book/parameterized-algorithms.pdf and at the chapter about tree decomposition I am trying to ...
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1 vote
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### Polynomial kernelization for Set Splitting

In a set system $(U, F)$, $F\subseteq \mathcal{P}(U))$, we say that a function $f: U \to \{0, 1\}$ is a coloring of $(U, F)$. A set in $F$ is split by $f$ if $F$ receives both colors. The Set ...
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### Prerequisites for studying parametrized complexity

Which areas of CS/Math should one have mastered before diving into parametrized complexity?
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### Finding a kernel for d-Bounded degree deletion

In $d$ Bounded degree deletion problem, we are given an undirected graph $G$ and a positive integer $k$, and the task is to find at most $k$ such vertices whose removal decreases the the maximum ...
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### What does a kernel of size n,n^2 ,... mean?

So according to Wikipedia, In the Notation of [Flum and Grohe (2006)], a ''parameterized problem'' consists of a decision problem $L\subseteq\Sigma^*$ and a function $\kappa:\Sigma^*\to N$, the ...
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1 vote
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### Is there an NP-hard problem for which no Fixed-Parameter Tractable algorithm exists?

Question Is there an NP-hard problem for which we can add a parameter1 to create a "natural"2 parametrised problem for which no FPT algorithm exists? The adding a parameter is needed ...
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