Skip to main content
Share Your Experience: Take the 2024 Developer Survey

Questions tagged [set-cover]

The tag has no usage guidance.

83 questions
Filter by
Sorted by
Tagged with
0 votes
1 answer
26 views

How can I optimize the assignment of object sets to workers with pre-existing caches to minimize discrepancy?

I am working on a problem where I have $n$ workers, each with a cache that already contains a specific set of objects. Additionally, I receive $n \times m$ sets of objects. My task is to assign ...
• 33
1 vote
0 answers
45 views

Is the Maximum Coverage Problem Remains as Hard when Taking Most Sets?

In the maximum coverage problem (also known as max k-cover) we are given a universe $U = \{e_1,\ldots, e_n\}$ of elements, a collection $F = \{S_1,\ldots, S_m\} \subseteq 2^U$ of sets over $U$, and an ...
• 412
2 votes
1 answer
79 views

Set Cover with Multiple covers

I am interested in whether a set cover instance that covers all elements $q$ times may have the property that every sufficiently small subset of this set cover will not cover the elements even once. ...
• 412
1 vote
1 answer
116 views

2 votes
0 answers
42 views

Geometric Set Cover Problem and Union Complexity

I have encountered an instance of the Geometric Set Cover problem where the complexity of the union of any subset with size, say k, of m objects is linear with respect to m. I am aware of a well-known ...
5 votes
0 answers
62 views

W[t]-containment of partial covering problems

I would like to know more about the W[t]-containment of partial covering problems. Especially, I am interested in the question whether Partial Set Cover (Problem Definition at the end of the question) ...
• 81
0 votes
1 answer
73 views

Complexity of Exact Cover problem if containing a Set Cover means there is an Exact Cover

As stated in the question, I'm interested in a variant of Exact Cover that is currently relevant to my research. Specifically, a variant where you are promised that if there is a Set Cover of size $k$,...
2 votes
0 answers
67 views

Confusion with the definition of Online Set Cover

I am confused on a technicality on how Online Set Cover is defined. One way to define it is: We are given a collection of sets $\mathcal{S}$ upfront, and in each time-step an element arrives to be ...
• 607
0 votes
0 answers
129 views

Approximate inclusion-Exclusion?

I am trying to understand or find literature on the following problem of approximate inclusion exclusion. Let $S:=\{A_i\}_{i=1}^{m}$ be a set of $m$ sets. Every intersection of $k$ elements in $S$ ...
• 716
1 vote
1 answer
85 views

Set cover with rewards

I am dealing with the following problem: Given a universe $U$, let $\mathcal{S}$ be a family of subsets of $U$. Each subset $S\in\mathcal{S}$ is associated with a non-negative reward, and each element ...
0 votes
0 answers
80 views

A Simpler Solution for a special case of the Set Cover problem

We decomposed a simple polygon into many small regions. Then we estimated a visibility polygon of a point by a subset of the small regions. Now I need the minimum set of visibility polygons that can ...
0 votes
1 answer
63 views

Set cover where consecutive sets differ by at most one item [closed]

First I define my version of the set cover problem: We have a collection of sets such as $S_1, \dots, S_m$ where each $S_i$ is a subset of $M=\{1,\dots, m\}$. The goal is to find the minimum number of ...
• 230
0 votes
0 answers
79 views

"Fast" approximation algorithm for geometric hitting set of same-height rectangles

In the Geometric Hitting Set problem, we are given a set of $m$ geometric objects and a set of $n$ points in $\mathbb{R}^2$, and we wish to find a small subset of the points that hits all the objects. ...
• 2,153
2 votes
1 answer
77 views

2 votes
1 answer
108 views

Can the Banach-Tarski paradox be "realized" by floating-point round-off?

The Banach-Tarski paradox says that a ball in $\mathbb{R}^3$ can be partitioned into a finite number of pieces, whose rearrangement has a larger volume than the original. It occurred to me that it ...
• 3,753
3 votes
0 answers
79 views

• 101
6 votes
1 answer
223 views

Minimal generator for a set of sets

Is this a known problem? Given a set of sets $S$ find a set of sets $B$ s.t. each set in $S$ can be obtained through unions of some sets in $B$. The set $S$ is already a solution but the objective is ...
• 1,322
0 votes
1 answer
93 views

Polynomial approximation algorithm for set cover with assumption

We want to cover $n$ elements with some sets from $S_1, …, S_m$ (classical set cover). We furthermore suppose that any element belongs to at least $k$ sets and want to find a set cover with cardinal ...
• 129
2 votes
1 answer
163 views

About a pre-processing step for primal–dual weighted set cover problem

I was reading the paper titled "Primal-dual RNC approximation algorithms.." by Rajagopalan and Vazirani. I have a problem of understanding the Lemma 4.1.1. They present a dual fitting based algorithm ...
11 votes
0 answers
395 views

Error in paper "Some NP-complete geometric problems"?

The paper in question: M.R. Garey, R.L. Graham and D.S. Johnson. Some NP-complete geometric problems . This paper proofs the NP-completeness of some well-known problems, such as the Steiner Tree ...
• 275
-1 votes
1 answer
87 views

Restricted Universe Exact Cover

Apologies for a simple question - I am a beginning graduate student in TCS. Consider the following $\mathrm{ExactCover}$ problem: Given a collection $\mathcal{S}$ of subsets of a universe set $U$ and ...
• 15
0 votes
1 answer
1k views

Definition of k-set cover

I'm trying to understand the sparsification lemma by Impagliazzo, Paturi and Zane (IPZ) (from this article) and in their proof they reduce the k-SAT problem to the k-set cover problem. But their ...
3 votes
1 answer
77 views

Complexity of Finding Optimal Synergistic Set Packings

Motivation: While developing tools for fast execution of machine learning workflows, we realized that many workflows require intermediate results -- sometimes we should cache these results, and ...
• 133
1 vote
1 answer
114 views

Set cover by alternative of sets

I had this question when looking at problem C on this morning's code jam: Suppose you have a set $S$ and $N$ pairs of subsets $\{S_i^0, S_i^1\}$, $S_i^j\subset S.$ Does there exist a cover of $S$ ...
• 213
2 votes
0 answers
122 views

Alternative Set Cover Algorithm With Doubling

I remember that I saw once an alternative to the greedy set cover algorithm that works as follows: Assign weight 1 to every element in the universe. Repeat steps 2 and 3 until the universe is covered:...
• 121
4 votes
0 answers
199 views

Approximating set cover when it is known that an exact set cover exists

Suppose $U = \{1, 2, \cdots, n\}$ is a universe and $\mathcal S = \{S_1, S_2, \cdots, S_m\}$ is a collection of sets such that each set contains exactly $c$ elements, where $c$ is a constant. In this ...
• 227
2 votes
1 answer
1k views

Partial cover approximation

We have a set of elements $E=\{e_1, e_2, \ldots, e_m\}$, and $n$ subsets of $E$: $S_1, S_2, \ldots, S_n$ The union of those subsets is $E$, and each subset $S_i$ has a non-negative weight $w_i$. The ...
3 votes
1 answer
456 views

What is the reverse of greedy algorithm for setcover?

A common approach to approximating SETCOVER is the greedy algorithm (Algorithm 2.2 Vazirani). This algorithm greedily picks the most cost-effective subset at each iteration, removes covered elements, ...
5 votes
1 answer
1k views

Is there an approximation algorithm for MAX k DOUBLE SET COVER?

Given a set system $(X,\mathcal S)$, let us say that a subset $\mathcal C\subseteq \mathcal S$ doubly covers a vertex $x$ in $X$ if $x$ is contained in at least two sets of $\mathcal C$. Let us define ...
• 2,153
2 votes
1 answer
565 views

Counting distinct set covers

I'm given a universal set $N = \{1, 2, \dots, n\}$, a family of sets $\mathcal{F} = \{ S_1, S_2, \dots, S_m \}$, $S_i \subseteq N$, and I need to count the number of distinct ways to cover the ...
5 votes
1 answer
683 views

Bipartite Graphs - Maximum subset of one partition with at most n neighbours - NP-hard?

Given: A bipartite graph G=(U,V,E) Integers n and k. Decision Problem: Is there a subset of U of size k that has at most n neighbours? I am trying to figure out whether this problem is NP-hard (...
0 votes
0 answers
26 views

Optimizing distribution of load

I want to run $k$ programs distributed on $N$ machines. Because of resource constraints, a machine can have at most $p$ of the $k$ programs installed. To have a balanced system, I can install each of ...
2 votes
0 answers
92 views

• 103
7 votes
1 answer
683 views

• 171
-1 votes
1 answer
128 views

Combinatorial algorithm for load balancing

I have a problem that can be solved with linear programming, but I'm hoping there's a combinatorial algorithm for this (even approximation is fine). This is basically a load balancing problem using ...
11 votes
1 answer
951 views

Set Cover with bounded intersection size

So, the set cover problem is trivial if none of the candidate sets intersect eachother. However, what if the size of the intersection for any pair of candidate sets was at most 1? Is this problem NP-...