# Questions tagged [set-cover]

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### What are the real world applications of set cover problem?

I am studying about set cover problem and wondering that which problems in real world can be solved by set cover. I found that IBM used this problem for their anti-virus problem, so there should be ...
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### Variation on weighted set cover, cover by consecutive pairs

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 $B \subseteq N$. ...
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### Is 'double max-$k$ vertex-cover' NP-hard?

Consider the following problem, which I have called '$\mathsf{\text{double max$k$-vertex-cover}}$': Given an undirected graph $G=(V,E)$ and integers $k$ and $t$, does there exist a set of vertices ...
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### Vertex cover algorithms for directed graphs?

I've recently been working on a problem that I believe can be expressed as a vertex cover problem over a directed graph. Formally, I have a graph $G = (V,E)$ where $V$ is a vertex set and $E$ is a ...
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### Minimum number of shopping trips for a group of people to buy presents for each other

We have a group of $n$ people. We are given a list of who must buy presents for whom within the group. Each person might need to buy/receive any number of presents, or possibly none at all. In a ...
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### Is this variant of set cover NP-complete?

Let's say we have a universe $U$ of $n$ elements and a collection $S$ of $m$ subsets of $U$, i.e., $S=\{S_1,\ldots,S_m\}$, and a positive integer $k$. If I ask "is there a set cover of $U$ of size $k$ ...
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### Approaches to the size constrained weighted set cover problem

I am trying to solve a weighted set cover problem where the number of selected subsets is limited by a constant $k$. Assuming this is a pretty straight-forward variation of weighted set cover I ended ...
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### How can I convert a list with duplicates into a set for a reduction to the set cover problem?

I'm trying to come up with a reduction for a problem whose description is more or less identical to the first problem given here. Here's a condensed version of the problem: You're given a collection ...
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### Hardness of a problem related to set cover

Suppose $C_1, \ldots, C_m$ are subsets of $\{1, \ldots, n\}$. The goal is to find the smallest subcollection of $C_1, ..., C_m$ such that each element of $\{1, \ldots, n\}$ appears at least $k$ times ...
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### Greedy algorithm for Set Cover problem - need help with approximation

I want to approximate how close is the greedy algorithm to the optimal solution for the Set Cover Problem, which I'm sure most of you are familiar with, but just in case, you can visit the link above. ...
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### Reduction from a further constrained problem

If I find an NP Hard problem that is equivalent to my problem with an additional constraint or bound, can I still prove that my problem is NP Hard? Generally, this is probably not the case. For ...
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### How to enumerate minimal covers of a set

I have a set $S$ and a set $P = \{P_{1},...,P_{n}\}$ with $\bigcup P_{i} = S$. I want to find all the inclusion-minimal subsets of $P$ that are covers of $S$. What is the best algorithm for ...
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### Proving NP-hardness of strange graph partition problem

I am trying to show the following problem is NP-hard. Inputs: Integer $e$, and connected, undirected graph $G=(V,E)$, a vertex-weighted graph Output: Partition of $G$, $G_p=(V,E_p)$ obtained ...
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### Set cover problem with constant size subset

Consider a variation of the set cover problem in which the size of the subsets is no larger than a constant $k$. Is this variation still NP-hard?
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### Transition coverage for a DFA

Let $G$ be a directed graph, with a single source node $s$. I want to find a collection of paths that cover every edge of $G$ (i.e., every edge of $G$ appears in at least one of these paths), where ...
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### Finding an instance of an n-element set cover

Below is a homework problem where we have been asked to alter a greedy algorithm to return n element instance of a set problem. The original algorithm is also below. I was thinking that I could alter ...
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### Time Complexity of a selection problem

I wonder what's the time complexity of the following selection problem I found while thinking of a string-matching problem. [Assuming operations on integers take $O(1)$ time] We are Given $m$ sets, ...
Given is a planar graph $G=(V,E)$ and let $\mathcal{G}$ denote its embedding in the plane s.t. each edge has length $1$. I have furthermore a set $C$ of points where each point $c \in C$ is contained ...
I need an efficient algorithm that takes input a collection of intervals and outputs the largest subset of non-intersecting intervals. i.e. Given a set of intervals $I = \{I_1, I_2, \ldots, I_n\}$ ...