Interactive Proofs and the Hardness of Approximating Cliques
E17354
"Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Interactive Proofs and the Hardness of Approximating Cliques canonical | 1 |
| “Some optimal inapproximability results” | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T143823 — 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: Interactive Proofs and the Hardness of Approximating Cliques Context triple: [Shafi Goldwasser, notableWork, Interactive Proofs and the Hardness of Approximating Cliques]
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A.
The Knowledge Complexity of Interactive Proof Systems
"The Knowledge Complexity of Interactive Proof Systems" is a seminal theoretical computer science paper that introduced the notion of zero-knowledge proofs, fundamentally shaping modern cryptography and complexity theory.
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B.
Randomness and Computation
"Randomness and Computation" is Shafi Goldwasser's influential doctoral thesis that helped lay the foundations of modern complexity theory and cryptography by rigorously exploring the role of randomness in efficient computation.
-
C.
Probabilistic Encryption
Probabilistic Encryption is a cryptographic technique that uses randomness in the encryption process so that the same message encrypts to different ciphertexts, enhancing security against attackers.
-
D.
New Directions in Cryptography
New Directions in Cryptography is a landmark 1976 paper that introduced the concepts of public-key cryptography and digital signatures, fundamentally reshaping modern cryptography and secure communications.
-
E.
Kalai–Smorodinsky bargaining solution
The Kalai–Smorodinsky bargaining solution is a cooperative game theory concept that selects a fair agreement between parties by preserving proportional gains relative to their best possible outcomes.
- 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: Interactive Proofs and the Hardness of Approximating Cliques Target entity description: "Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
-
A.
The Knowledge Complexity of Interactive Proof Systems
"The Knowledge Complexity of Interactive Proof Systems" is a seminal theoretical computer science paper that introduced the notion of zero-knowledge proofs, fundamentally shaping modern cryptography and complexity theory.
-
B.
Randomness and Computation
"Randomness and Computation" is Shafi Goldwasser's influential doctoral thesis that helped lay the foundations of modern complexity theory and cryptography by rigorously exploring the role of randomness in efficient computation.
-
C.
Probabilistic Encryption
Probabilistic Encryption is a cryptographic technique that uses randomness in the encryption process so that the same message encrypts to different ciphertexts, enhancing security against attackers.
-
D.
New Directions in Cryptography
New Directions in Cryptography is a landmark 1976 paper that introduced the concepts of public-key cryptography and digital signatures, fundamentally reshaping modern cryptography and secure communications.
-
E.
Kalai–Smorodinsky bargaining solution
The Kalai–Smorodinsky bargaining solution is a cooperative game theory concept that selects a fair agreement between parties by preserving proportional gains relative to their best possible outcomes.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
research paper
ⓘ
theoretical computer science paper ⓘ |
| assumes | standard complexity assumptions such as P not equal to NP ⓘ |
| contribution |
established that near-maximum cliques are hard to approximate
ⓘ
influenced later work on PCP theorem and inapproximability ⓘ introduced powerful interactive proof techniques for hardness of approximation ⓘ linked interactive proofs with approximation complexity ⓘ |
| establishes |
gap between exact and approximate solutions for clique
ⓘ
hardness of distinguishing graphs with large cliques from graphs with only small cliques ⓘ |
| field |
computational complexity theory
ⓘ
theoretical computer science ⓘ |
| focusesOn |
gap-introducing reductions
ⓘ
inapproximability results ⓘ maximum clique problem ⓘ probabilistically checkable proofs ⓘ |
| impact |
seminal work in hardness of approximation
ⓘ
widely cited in theoretical computer science literature ⓘ |
| influenced |
development of PCP-based hardness techniques
ⓘ
subsequent research on inapproximability of combinatorial problems ⓘ |
| mainTopic |
NP-hardness of approximation
ⓘ
approximation algorithms ⓘ clique problem ⓘ hardness of approximation ⓘ interactive proofs ⓘ |
| motivation |
exploring power of interactive proofs beyond decision problems
ⓘ
understanding limits of efficient approximation algorithms ⓘ |
| problemDomain |
combinatorial optimization
ⓘ
graph optimization ⓘ |
| provesAbout |
approximation ratio for maximum clique
ⓘ
limits of polynomial-time approximation algorithms ⓘ |
| relatedTo |
NP-completeness
ⓘ
PCP theorem ⓘ graph theory ⓘ optimization problems ⓘ |
| resultType | hardness of approximation theorem ⓘ |
| shows |
interactive proof techniques can yield hardness of approximation results
ⓘ
it is computationally hard to approximate maximum clique within certain factors ⓘ strong inapproximability bounds for clique ⓘ |
| usesTechnique |
PCP-style constructions
ⓘ
gap amplification ⓘ interactive proof systems ⓘ randomized reductions ⓘ |
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: Interactive Proofs and the Hardness of Approximating Cliques Description of subject: "Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
“Some optimal inapproximability results”