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gptkbp:instanceOf
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gptkb:theoretical_computer_science
gptkb:NP-complete_problem
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gptkbp:approximationRatio
|
ln(n)
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gptkbp:category
|
gptkb:mathematical_optimization
covering problem
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gptkbp:complexity
|
NP-complete
|
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gptkbp:definedIn
|
Given a universe and a collection of its subsets, find the smallest sub-collection whose union is the universe.
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gptkbp:describedYear
|
1972
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gptkbp:estimatedCost
|
greedy algorithm
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gptkbp:field
|
gptkb:mathematics
computer science
|
|
gptkbp:firstDescribed
|
gptkb:Richard_Karp
gptkb:Karp's_21_NP-complete_problems
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gptkbp:generalizes
|
vertex cover
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gptkbp:hardnessOfApproximation
|
cannot be approximated within (1-o(1)) ln n unless P=NP
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gptkbp:hasSpecialCase
|
hitting set
set packing (dual problem)
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gptkbp:hasVersion
|
Does there exist a cover of size k?
|
|
gptkbp:input
|
collection of subsets
universe of elements
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|
gptkbp:output
|
smallest sub-collection covering the universe
|
|
gptkbp:relatedTo
|
gptkb:combinatorics
gptkb:approximation_algorithm
optimization
vertex cover
hitting set
|
|
gptkbp:usedIn
|
gptkb:machine_learning
bioinformatics
resource allocation
data mining
network design
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gptkbp:bfsParent
|
gptkb:Reducibility_Among_Combinatorial_Problems_(Karp,_1972)
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gptkbp:bfsLayer
|
6
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|
https://www.w3.org/2000/01/rdf-schema#label
|
Set Cover
|