# Questions tagged [np-hardness]

Questions related to NP-hardness and NP-completeness.

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### A version of bipartite graph turnpike problem

Given a set of "required" weights for edges of a bipartite graph, I am looking for assignments to the nodes so that there is at least an edge carrying a weight from that set. Each edge can have ...
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### Complexity of a weighted subset selection problem.

I'm currently thinking about a problem I'd like to manage in one of my applications. There is a set of objects $\{A, B, C, D, \ldots\}$. Every object has the same attributes with different values. ...
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### For which values of $k$ is the $k$-disjoint paths problem in $\mathcal{P}$?

The $k$-Vertex-Disjoint Paths Problem ($k$-$\text{DPP}$) is defined as follows: Input: A graph $G=(V,E)$ and $k$ pairs of vertices $(s_1,t_1),\ldots,(s_k,t_k)$. Question: Does there exist $k$-...
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### NP-hard problem on planar unit disk graph

I am curious to know whether there are problems which are np-hard even on planar unit disk graphs. A unit disk graph is the intersection graph of a collection of unit disks in the plane, where we ...
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### What are some example problems for integer programming that are *not binary*

I'm interested in NP-hard problems that have a "nice" integer-programming formulation (quadratic or linear, with quadratic or linear constraints) that is not binary. Of course it is always possible ...
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### Is the nonnegativeness of a polynomial hard for $\mathsf{NP}_\mathbb{R}$?
It is clear that the following problem is in $\mathsf{NP}_\mathbb{R}$. Input: a list $P$ of triplets $(a,s,t)$ where $s$ and $t$ are nonnegative integers. Output: is there an $x\in \mathbb{R}$ such ...
Consider the following problem: Let there be a set A of $n$ items $A=\{z_1, ..., z_n\}$, and let $W$ be a strictly positive integer. Each item $z_i$ has a value $v_i$ and a weight $w_i$. Finding a ...