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Questions tagged [set-cover]

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5
votes
1answer
315 views

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 ...
5
votes
2answers
6k views

Algorithm to return largest subset of non-intersecting intervals

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 $I = \{I_1, I_2, \ldots, I_n\}$ ...
15
votes
1answer
413 views

Grid covering by rectangles

We have a $N_1 \times N_2$ grid. We have a collection of rectangles on this grid, each rectangle can be represented as a $N_1$-by-$N_2$ binary matrix $R$. We want to cover the grid with those ...
1
vote
2answers
704 views

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 ...
5
votes
3answers
1k views

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 ...
5
votes
1answer
2k views

Variation of Set Cover Problem: Finding a maximum-sized collection of disjoint set-covers

I have the following problem, which seems to be similar to Set Cover. We are given a set $U$ of elements (the universe, e.g., $U=\{1,2,3,4,5\}$). We're also given a set $S$ of subsets (e.g., $S=\{\{1\...
4
votes
1answer
143 views

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 ...
4
votes
1answer
120 views

Path cover with paths of bounded length, in the plane

I have a weighted, undirected, Euclidean complete graph $G$, a special vertex $r$, and an upper bound $b$. I want to find a minimum-cost path cover that covers all vertices of $G$, subject to the ...
3
votes
1answer
150 views

Maximum minimal set coverage

Suppose we are given a universal set $U$ and a family of subsets of $U$, denoted by $F$ (elements in $F$ are subsets of $U$). We assume that all elements in $F$ can cover $U$, i.e., $U\subseteq \...
1
vote
1answer
385 views

Set cover problem with sets of size 2

I have a question about the Set Cover problem: If I get a universe $U$, and $m$ subsets of size exactly $2$, and an integer $k$. Is this problem is still NP-C or I can solve it on a polynomial time? ...
1
vote
1answer
219 views

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 ...
1
vote
1answer
227 views

Maximum weighted disjoint set union

I would like to know whether the following problem is a standard problem that has been considered in the research literature. I performed some searches, which have not produced results. I call this ...
0
votes
1answer
44 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 ...