# Questions tagged [set-cover]

Set cover is a well-known NP-complete problem: given a collection of sets, find as small as possible a subcollection whose union is the same as the union of the entire collection.

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### Minimal edge cover of the hypergraph

We know that minimal edge cover for the normal graph is polynomial time solvable. Is it also true for hypergraph?
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### Reduce Clique to Set Cover

Is it possible directly to reduce clique to set cover? I know that there are some ways of direct reduction from Clique to Vertex Cover and from Vertex Cover to Set Cover, so I am very interested to ...
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### Minimum Dominating Set

Consider a graph $G$ with minimum degree $d$, we know through sets cover, it's possible to find the one dominating set $S$ that covers $G$ such that $$S\leq O(\log n)\frac{n}{d}$$ with high ...
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### Point of Interest Problem

You are in a xy plane with a set of points F. You also have a collection P of N sets { P1,...., Pn} where each of the set consist of points of the form (Px,Py). Each set has a different number of ...
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### Set Cover with multiple covers

In the Set Cover problem we need to cover each element at least once. I'm considering the case where I want each element to be covered at least $k$ times with constant $k$. I consider the classic LP ...
Input: A set $N = \{1, \dots, n\}$, subsets/consecutive pairs $S_1 = \{1,2\}, \dots, S_n = \{n,1\}$ with associated costs $c_1, \dots, c_n \in \mathbb{N} \cup \{0\}$, and a subset $B \subseteq N$. ...