"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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| "Reducibility Among Combinatorial Problems" (1972) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5429796 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: "Reducibility Among Combinatorial Problems" (1972) Context triple: [Richard Karp, notableWork, "Reducibility Among Combinatorial Problems" (1972)]
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A.
P, NP, and NP-Completeness: The Basics of Complexity Theory
"P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
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B.
Cook–Levin theorem
The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.
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C.
“Inapproximability results for SAT and other problems”
“Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
-
D.
“Molecular computation of solutions to combinatorial problems”
“Molecular computation of solutions to combinatorial problems” is Leonard Adleman’s pioneering 1994 paper that introduced DNA computing by demonstrating how molecular biology techniques can solve a combinatorial search problem.
-
E.
"The Complexity of Theorem-Proving Procedures"
"The Complexity of Theorem-Proving Procedures" is Stephen Cook’s landmark 1971 paper that introduced the concept of NP-completeness and proved the Boolean satisfiability problem (SAT) to be NP-complete, laying the foundation for modern computational complexity theory.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: "Reducibility Among Combinatorial Problems" (1972) Target entity description: "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.
-
A.
P, NP, and NP-Completeness: The Basics of Complexity Theory
"P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
-
B.
Cook–Levin theorem
The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.
-
C.
“Inapproximability results for SAT and other problems”
“Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
-
D.
“Molecular computation of solutions to combinatorial problems”
“Molecular computation of solutions to combinatorial problems” is Leonard Adleman’s pioneering 1994 paper that introduced DNA computing by demonstrating how molecular biology techniques can solve a combinatorial search problem.
-
E.
"The Complexity of Theorem-Proving Procedures"
"The Complexity of Theorem-Proving Procedures" is Stephen Cook’s landmark 1971 paper that introduced the concept of NP-completeness and proved the Boolean satisfiability problem (SAT) to be NP-complete, laying the foundation for modern computational complexity theory.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf | scientific paper ⓘ |
| author |
Richard Karp
NERFINISHED
ⓘ
Richard M. Karp NERFINISHED ⓘ |
| basedOn | Cook–Levin theorem NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
Chromatic Number problem ⓘ Clique problem ⓘ Exact Cover by 3-Sets problem NERFINISHED ⓘ Exact Cover problem NERFINISHED ⓘ Feedback Vertex Set problem NERFINISHED ⓘ Hamiltonian Cycle problem NERFINISHED ⓘ Hitting Set problem NERFINISHED ⓘ Job Sequencing problem (NP-complete variant) NERFINISHED ⓘ Knapsack problem NERFINISHED ⓘ Node Cover problem ⓘ Partition problem ⓘ Satisfiability problem ⓘ Set Covering problem NERFINISHED ⓘ Set Packing problem NERFINISHED ⓘ Steiner Tree problem (decision version) NERFINISHED ⓘ Subset Sum problem NERFINISHED ⓘ Traveling Salesman problem (decision version) NERFINISHED ⓘ 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 NERFINISHED ⓘ |
| publisher | Plenum Press NERFINISHED ⓘ |
| 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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: "Reducibility Among Combinatorial Problems" (1972) Description of subject: "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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.