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gptkbp:instanceOf
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computational complexity theory concept
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gptkbp:category
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theoretical computer science
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gptkbp:complexity
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NP
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gptkbp:defines
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A problem is NP-complete if every problem in NP can be reduced to it in polynomial time.
A decision problem is NP-complete if it is in NP and as hard as any problem in NP.
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gptkbp:describedBy
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gptkb:Cook's_theorem
gptkb:Cook-Levin_theorem
gptkb:Levin's_theorem
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gptkbp:example
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gptkb:Hamiltonian_cycle_problem
gptkb:3-SAT
gptkb:Clique_problem
gptkb:Graph_coloring_problem
gptkb:Subset_sum_problem
gptkb:Traveling_salesman_problem_(decision_version)
gptkb:Vertex_cover_problem
Boolean satisfiability problem
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gptkbp:field
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gptkb:mathematics
computer science
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gptkbp:firstProblem
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Boolean satisfiability problem
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https://www.w3.org/2000/01/rdf-schema#label
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NP-completeness
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gptkbp:importantFor
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central to computational complexity theory
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gptkbp:introduced
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gptkb:Stephen_Cook
gptkb:Leonid_Levin
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gptkbp:introducedIn
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1971
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gptkbp:namedFor
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gptkb:Richard_Karp
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gptkbp:notablePublication
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gptkb:Reducibility_Among_Combinatorial_Problems_(Karp,_1972)
gptkb:The_Complexity_of_Theorem-Proving_Procedures_(Cook,_1971)
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gptkbp:openProblem
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gptkb:P_vs_NP
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gptkbp:property
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If any NP-complete problem can be solved in polynomial time, all problems in NP can be.
If any NP-complete problem is not in P, then P ≠ NP.
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gptkbp:reductionType
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polynomial-time reduction
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gptkbp:relatedTo
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gptkb:P_vs_NP_problem
gptkb:NP-hardness
NP
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gptkbp:seeAlso
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gptkb:Karp's_21_NP-complete_problems
gptkb:Cook-Levin_theorem
gptkb:NP-hardness
P-completeness
Polynomial-time reduction
co-NP-completeness
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gptkbp:symbol
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gptkb:NPC
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gptkbp:bfsParent
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gptkb:Richard_M._Karp
gptkb:complexity_theory
gptkb:Algorithms_and_Complexity
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gptkbp:bfsLayer
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4
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