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.
Aliases (1)
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
research paper
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theoretical computer science paper → |
| assumes |
standard complexity assumptions such as P not equal to NP
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|
| contribution |
established that near-maximum cliques are hard to approximate
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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
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hardness of distinguishing graphs with large cliques from graphs with only small cliques → |
| field |
computational complexity theory
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theoretical computer science → |
| focusesOn |
gap-introducing reductions
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inapproximability results → maximum clique problem → probabilistically checkable proofs → |
| impact |
seminal work in hardness of approximation
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widely cited in theoretical computer science literature → |
| influenced |
development of PCP-based hardness techniques
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subsequent research on inapproximability of combinatorial problems → |
| mainTopic |
NP-hardness of approximation
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approximation algorithms → clique problem → hardness of approximation → interactive proofs → |
| motivation |
exploring power of interactive proofs beyond decision problems
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understanding limits of efficient approximation algorithms → |
| problemDomain |
combinatorial optimization
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graph optimization → |
| provesAbout |
approximation ratio for maximum clique
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limits of polynomial-time approximation algorithms → |
| relatedTo |
NP-completeness
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PCP theorem → graph theory → optimization problems → |
| resultType |
hardness of approximation theorem
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|
| shows |
interactive proof techniques can yield hardness of approximation results
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it is computationally hard to approximate maximum clique within certain factors → strong inapproximability bounds for clique → |
| usesTechnique |
PCP-style constructions
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gap amplification → interactive proof systems → randomized reductions → |
Referenced by (2)
| Subject (surface form when different) | Predicate |
|---|---|
|
Johan Håstad
("“Some optimal inapproximability results”")
→
Shafi Goldwasser → |
notableWork |