Questions tagged [np]
In computational complexity, NP is the complexity class consisting of problems whose yes instances can be verified in polynomial time. NP stands for 'nondeterministic polynomial time '.
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How to determine if a set is a sumset
Let $G$ be a commutative group (assume whatever you want on $G$ if needed. I am mainly interested in $G = \mathbb{Z}/n\mathbb{Z}$).
Let $k$ be a fixed integer.
Let $(a_1, \dots, a_{k^2})$ be a list of ...
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Any updates on "The minimum cost perfect matching problem with conflict pair constraints"?
The subject of the paywalled article The minimum cost perfect matching problem with conflict pair constraints (MCPMPC) are perfect matchings of minimum cost that do not contain certain pairs of edges; ...
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Quasi polynomial algorithm for NP complete problem [closed]
I know that quasi polynomial algorithm is neither polynomial nor exponential. But I want to know if we find such algorithm for NP complete problem, will it be of any use? Or is there such algorithm ...
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Prove the NP-hardness of the following problem: Whether there exists a partition for a set of data points
Can anybody help me prove the NP-hardness of the following question:
Given $x_0, x_1, ..., x_m \in \mathbb{R}^n$, determine whether there exists a partition $S\cup [m]\backslash S$, such that $x_0 \in ...
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Is there a version of 3-SAT that is NP-complete but grows like $2^n$ instead of $2^{n \choose 3}$?
If I have $n$ variables and I want to write down all 3-SAT problems, the number of problems is $2^{8{n \choose 3}}$, since each clause has 3 variables and each variable can be negated or not.
But ...
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Complexity of finding single source paths with capacity constraints and length constraints
Let $G=(V,A)$ be a directed graph with distinguished vertex $s\in V$ and let $c:A\rightarrow{\mathbb N}$ denote arc capacities. For any $t\in V,t\not=s$ we are given two numbers: $C_{t},L_{t}$. Let $...
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The hardness of active learning with fixed budget
I have been looking for theoretical papers studying this question of the fundamental hardness of PAC active learning algorithms. I found a few papers studying the problem from a fixed perspective (...
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Hardness of an optimization problem when some variables are fixed
Given a general optimization problem, I would like to know what we can say about the hardness of the problem when a subset of its variables are fixed.
With the two (related) examples, it is clear that ...
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Can we say this nonlinear integer programming problem is NP-hard?
I was wondering if the following nonlinear integer programming problem is NP-hard or not.
$$\max_{x_i \in \{0,1\}} \frac{\sum_{i=1}^{n}a_i x_i}{\sqrt{\sum_{i=1}^{n}b_i x_i}}$$
such that $\sum_{i=1}^{n}...
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Using Kolmogorov complexity to measure difficulty of problems?
We call the natural number $n$ a partition number $\iff$
$$
\exists d | n: \gcd\left(d,\frac{n}{d}\right)=1 \text{ and } \Omega(d) = \Omega\left(\frac{n}{d}\right)\;,
$$
where $\Omega$ counts the ...
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Is it NP-hard to find the min set of nodes in a graph so that the set of paths joining them cover all the nodes?
Given a directed graph $G=(V,A)$ and given for every pair of nodes $(i,j)$
a valid path $P(i,j)=(v_1=i,...,v_l=j)$ on $G$.
Find a minimum set of nodes $M$ such that $\bigcup_{(i,j)\in M\times M}P(i,j)=...
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Modular square roots problem which is $NP$ hard
It is well known extracting modular square roots modulo a composite number factors the modulus.
On other hand given $u,v>0$ and an integer $n$, deciding if there is a factor of $n$ in $[u,v]$ is $...
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Path cover with sets of nodes
I am considering the following variant of the path-cover problem. I have an acyclic directed graph G=(V,E). Moreover, the set V is partitioned into $V=V_1 \cup ... \cup V_k$ (these sets are pairwise ...
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Compute the average path weights of paths with the same path length in a directed acyclic graph (DAG)
Given a weighted directed acyclic graph (DAG) $G=(V,E)$ with each edge $e\in E$ has a non-negative weight $w(e)$. For a path $p=(e_1,e_2,\dotsc,e_n)$ in $G$, define the path weight as : $w(p)=\sum_{i=...
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Traveling salesperson problem algorithm [closed]
I was wondering something, let's say in a symmetric distance matrix of a sample of TSP, there was a sure algorithm that could remove between 30% to 80% of the values (distances) that wouldn't ...
