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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.

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

NP-complete problems have two properties:

  1. They are in the NP complexity class (can be solved by nondeterministic Turing-machine)
  2. They are NP-hard (there is a reduction from any other NP problem to them)

A polynomial-time solution for any specific NP-complete problem will settle the $P=NP$ question affirmatively: any other problem in NP can be reduced to the specific problem of which a solution exists, and thus be solved.

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NP-hard problems but only for n≥3

2-SAT is in P; 3-SAT is NP-complete. Exact cover by 2-sets is in P; exact cover by 3-sets is NP-complete Two-dimensional matching is in P; three-dimensional matching is NP-complete Graph 2-coloring is trivially in P; graph 3-coloring is…
Mark Dominus
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Why is proving something is NP-complete useful, and where can I use it?

I trying to understand where, as a programmer in situations where it can be good to do a NP-complete reduction to prove that a problem is NP-complete, why is it good to do that as a programmer? I don't understand.
Jonte YH
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Why is the clique problem NP-complete?

Possible Duplicate: Is the k-clique problem NP-complete? I've been lately reading about the clique problem, specifically, the variety of the clique problem of deciding whether a given graph $G$ with $n$ nodes has a clique of at least size…
David Faux
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Negative numbers in Subset-Sum

If I have a set $A$ with positive and negative numbers, and a number to find C. It is possible to reduce the problem to one with only positive numbers in set $A$? I mean, it is possible to find a new set $A$ and a new number $C$, so $A$ were only…
Pedro
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Is "Solving two-variable quadratic polynomials over the Integers" is an NP-Complete Problem?

On this Wikipedia article, they claim that given $A, B, C \geq 0, \; \in \mathbb{Z}$, deciding whether there exist $x, \,y \geq 0, \, \in \mathbb{Z}$ such that $Ax^2+By-C=0$ is NP-complete? Given by how easy I can solve some (with nothing but…
DUO Labs
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Is set cover still NP-complete if you have a given k?

Set cover is NP-complete given an arbitrary set $U$, a set $S$ of subsets of $U$, and an integer $k$. However, what if $k$ is always a constant 3? Is that problem still NP-complete?
TheJKFever
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What does it mean when $A$ is a NP-Complete Problem but $\bar{A} = NP$?

I'm still in the process of grokking computational complexity. However, I came across a statement like the above in an old midterm paper I'm reviewing, and I'm not sure I completely follow its logic. $NP$ is the class of solveable decision…
Louis93
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looking for a strongly NP Complete related problem

I'm looking for a problem that is NP-Complete (even) if the number of input values is at most a polylog of the input size. So some or each value in the input should be so large that the number of values is "negligable". One way to do this is to say…
Albert Hendriks
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Game tournament program, NP complete?

I have been trying to find a solution both theoretical and practical to my problem but I just can't. The question is you have x players that should play some rounds y of games in groups of 4. Now if a player was in a game with somebody else, he is…
Hakaishin
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Is it NP complete to decide whether a graph has bigger clique or bigger independence number?

Is it $\mathsf{NP}$ complete to decide whether a graph $G$ has bigger clique $\omega(G)$ or bigger independence number $\alpha(G)$?
Turbo
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What do we know about the asymptotic proportion of "easy" instances of NP-complete problems

In practice, it seems that many NP-hard problems "usually" lead to easy instances, in the sense that a commercial solver can handle them reasonably. A few past questions on this topic (see here and here) have been answered by saying they are not…
Davis Yoshida
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Can a computational complexity class be redefined by using any complete (decision) problem?

Let $\mathcal{C}$ be a basic complexity class (such as $\mathrm{NP}, \mathrm{PSPACE}$). And $\mathcal{C}$ is closed under a reduction "$\leq$" (such as polynomial time many-one reduction "$\leq_{m}^{p}$", polynomial time Turing reduction…
Blanco
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Transforming 3 SAT to Simultaneous In-Congruence Problem?

Garey and Jhonson mentions that a 3-SAT Problem can be transformed to another NP-Complete Problem - Simultaneous incongruences (AN2): Given a collection $[(a_1,b_1),…,(a_n,b_n)]$ of ordered pairs of positive integers with $a_i≤b_i$ for $1≤i≤n$, is…
TheoryQuest1
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Show 1-in-3 SAT

1-in-3 SAT is the set of 3CNF formulas with no negated variables such that there is a satisfying assignment that makes exactly one variable in each clause true. Show 1-in-3 SAT is NP-complete Plan on doing a reduction from 3SAT. My confusion arises…
lars
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Is unary NP-Completeness equivalent to strong NP-Completeness?

I try to prove the equivalence between the two following properties of an NP-Complete problem $P$: (A) $P$ is unary NP-Complete if it is NP-Complete even if we encode the integers of the inputs with unary encoding. (B) $P$ is strongly NP-Complete if…
mouton5000
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