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NP-completeness

In computational complexity theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely, a problem is NP-complete when:

History, Known NP-complete problems & Properties

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Overview

Formal definition and related complexity classes

Known NP-complete problems

Solving NP-complete problems

Completeness under different types of reduction

History

Common misconceptions

Properties

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NP-completeness

Nodes95
Edges94
Triples15
Avg. degree1.98
Density0.021053
Components1

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NP-completeness

Top relations

related to history · 11
NP-completeness → At, Cook, John Hopcroft, Levin, Millennium Prize Problems, NP, NP-complete, STOC, The, The Clay Mathematics Institute, Turing
is a · 1
NP-completeness → logarithmic-space many-one reduction which is a many-one reduction that can be computed with only a logarithmic amount of space

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Important terminology

np-complete problems problem np time polynomial known polynomial-time solution algorithm quickly one solutions whether solve reductions class often computer verified

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
NP-completenessis alogarithmic-space many-one reduction which is a many-one reduction that can be computed with only a logarithmic amount of space0.90text
P-completeinstance ofThis type of reduction is more refined than the more usual polynomial-time many-one reductions and it allows us to distinguish more classes0.80text
A C 0instance ofAll currently known NP-complete problems remain NP-complete even under much weaker reductions0.80text
SAT are known to be complete even under polylogarithmic time projectionsinstance ofSome NP-Complete problems0.80text
NP-completenessrelated to historyThe0.60section
NP-completenessrelated to historyCook0.60section
NP-completenessrelated to historyLevin0.60section
NP-completenessrelated to historyNP-complete0.60section
NP-completenessrelated to historyAt0.60section
NP-completenessrelated to historySTOC0.60section
NP-completenessrelated to historyTuring0.60section
NP-completenessrelated to historyJohn Hopcroft0.60section

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