"Reducibility Among Combinatorial Problems" (1972)

E519559

"Reducibility Among Combinatorial Problems" (1972) is a landmark paper by Richard Karp that introduced NP-completeness to a broad audience by showing polynomial-time reductions among 21 classic combinatorial decision problems.

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Predicate Object
instanceOf scientific paper
author Richard Karp
Richard M. Karp
linked to: Richard Karp
basedOn Cook–Levin theorem
citationImpact highly cited paper in computer science
contribution established NP-completeness of many fundamental problems in graph theory and combinatorics
helped define the standard methodology for proving NP-completeness
popularized the notion of NP-completeness in computer science
showed polynomial-time reductions among 21 classic combinatorial decision problems
establishesNPCompletenessOf 3-Dimensional Matching problem
Chromatic Number problem
Clique problem
Exact Cover by 3-Sets problem
linked to: Exact Cover problem

Exact Cover problem
Feedback Vertex Set problem
Hamiltonian Cycle problem
Hitting Set problem
Job Sequencing problem (NP-complete variant)
Knapsack problem
Node Cover problem
Partition problem
Satisfiability problem
Set Covering problem
Set Packing problem
Steiner Tree problem (decision version)
Subset Sum problem
linked to: Subset sum problem

Traveling Salesman problem (decision version)
Vertex Cover problem
field computational complexity theory
computer science
theoretical computer science
influenced algorithm design and analysis
complexity-theoretic classification of combinatorial problems
development of NP-completeness theory
introducedConcept systematic use of polynomial-time many-one reductions among combinatorial problems
language English
publicationYear 1972
publishedIn Complexity of Computer Computations
publisher Plenum Press
status landmark paper in computational complexity theory
topic NP-complete problems
NP-completeness
combinatorial decision problems
polynomial-time reductions
usesConcept decision problem
many-one reduction
nondeterministic polynomial time
polynomial-time computable reduction

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Referenced by (7)

Full triples — surface form annotated when it differs from this entity's canonical label.

Richard Karp notableWork "Reducibility Among Combinatorial Problems" (1972)
NP-hardness historicalWork Karp's 21 NP-complete problems paper (1972)
linked to: "Reducibility Among Combinatorial Problems" (1972)
Karp reduction introducedInWork "Reducibility Among Combinatorial Problems"
subject linked to: Karp reductions
linked to: "Reducibility Among Combinatorial Problems" (1972)
Clique problem listedIn Karp's 21 NP-complete problems
linked to: "Reducibility Among Combinatorial Problems" (1972)
Clique problem publication Reducibility Among Combinatorial Problems
linked to: "Reducibility Among Combinatorial Problems" (1972)
Subset sum problem listedIn Karp's 21 NP-complete problems
linked to: "Reducibility Among Combinatorial Problems" (1972)
Computers and Intractability: A Guide to the Theory of NP-Completeness relatedTo Karp’s 21 NP-complete problems
linked to: "Reducibility Among Combinatorial Problems" (1972)