# Questions tagged [set-cover]

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### Specialized Algorithm for Set-Cover with $k=3$

I know that the Set-cover problem with $n$ elements and a universe of size $N$ is NP complete. Also, the problem is has parameterized complexity regarding the number of sets $k$ that should cover the ...
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36 views

### Weighted Set Cover Problem Minimizing Average Weight

In the traditional weighted set cover problem, we aim at minimizing the sum of the weight of the selected sets. Is there any problem/literature that aim at minimizing the average weight of the ...
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128 views

### 2-approximation edge-cover algorithm using primal-dual method

The problem Given an undirected graph $G=\left(V, E\right)$ and positive edge weights $w_e$, design a 2-approximation algorithm based on the primal-dual principle. So far I managed to represent the ...
1answer
118 views

### Given N sets of disjoint subsets, find a set of disjoint subsets such that it satisfies a criteria

Given a collection of sets $S_i$ of disjoint subsets $sub_i$ of a set $X$, find a set $A$ of disjoint subsets $asub$ such that each one of these subsets is subset or equal to at most one subset in ...
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50 views

### Given multiple families of sets, select a set from each such that the intersection of selected sets is a correspondence

Let $X = \{x_1, ... , x_k\}$ and $Y = \{y_1, ... , y_h\}$. A subset $S \subset X \times Y$ is a correspondence if : $\forall x, \exists y, (x,y) \in S$ and $\forall y, \exists x, (x,y) \in S$ That ...
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35 views

### On the complexity of Unique Coverage Problem restricted to geometrical settings

I come to you with a problem I have been struggling with for the past few weeks. I would like to classify (complexity) a special case of Unique Coverage. To set the mood on, I will start by ...
1answer
10 views

### Hardness of approximation statement clarification?

In the paper I'm reading, there is a hardness of approximation result for an algorithm proved using a reduction to set cover. Roughly, the claim states that if there existed an algorithm that solved ...
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### Algorithms for MinSat when all literals are positive?

I am given a set $U = \{1, \cdots, n\}$ and a set of subsets $C_1, \cdots, C_k$ of $U$; here the sets are all the same size. The minimum set-cover problem of course is to find the minimum number of ...
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31 views

### NP-hardness of maximum set cover with element-level submodular function

Consider the following generalization of maximum set cover problem: Given a collection $C$ of subsets of a finite set $S$. Find $C^{'} \subseteq C$ of cardinality $k$ that maximizes \[ \sum\...
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41 views

### Smallest set non-disjoint with other given sets

Given a number of sets, what is the best algorithm to calculate the smallest set S such that S is not disjoint with any of the given sets?
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12 views

### 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 ...
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21 views

### Weighted-Set Cover Approximation

So in the weighted-set cover problem, I need to determine the minimum weight cover. My algorithm calculates the efficiency for each set: ...
1answer
49 views

### set cover to edge cover

I want to find set cover of this problem. I have sets, each of cardinality 3. I want to find set cover. This is what I am doing. Treat each set as an edge, which is incident on each of its element. I ...
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70 views

### 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 $B \subseteq N$. ...