# Questions tagged [np-complete]

Questions about the hardest problems in NP, i.e. of those that can be solved in polynomial time by nondeterministic Turing machines.

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### Graph problem known to be $NP$-complete only under Cook reduction

The theory of NP-completeness was initially built on Cook (polynomial-time Turing) reductions. Later, Karp introduced polynomial-time many-to-one reductions. A Cook reduction is more powerful than a ...
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### Longest Repeated (Scattered) Subsequence in a String

Informal Problem Statement: Given a string, e.g. $ACCABBAB$, we want to colour some letters red and some letters blue (and some not at all), such that reading only the red letters from left to right ...
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### Covering a complete graph with n copies of an arbitrary graph: NP-complete?

Given a complete graph $G$, an arbitrary graph $H$, and a positive integer $n$, are there subgraphs $A_1,\dots,A_n$ of $G$ (not necessarily disjoint) such that their union is $G$, and each of them ...
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### Fastest known algorithm for $3$-$\mathrm{Partition}$ problem

$3$-$\mathrm{Partition}$ problem is $\mathsf{NP}$-Complete in a strong sense meaning there is no pseudo-polynomial time algorithm for it unless $\mathsf{P=NP}$. I am looking for the fastest known ...
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### A special case of the SUBSET SUM problem

Consider the following special case of SUBSET SUM Inputs: Positive integers $a$ and $b$ with $a \ne b$, and positive integers $k$ and $t$, with $k$ specified in unary. Encoding: These inputs (...