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Polynomial-time reduction

In computational complexity theory, a polynomial-time reduction is a method for solving one problem using another. One shows that if a hypothetical subroutine solving the second problem exists, then the first problem can be solved by transforming or reducing it to inputs for the second problem and calling the subroutine one or more times. If both the…

Completeness, Defining complexity classes & Types of reductions

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Overview

Types of reductions

Completeness

Defining complexity classes

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Polynomial-time reduction

Nodes38
Edges37
Triples24
Avg. degree1.95
Density0.052632
Components1

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Polynomial-time reduction

Top relations

related to Completeness · 13
Polynomial-time reduction → Every, EXPTIME-complete, For, Instead, NC, NL, NP, NP-complete, P-complete, Polynomial-time, PSPACE-complete, Therefore, To
related to Types of reductions · 2
Polynomial-time reduction → The, Turing
is a · 1
Polynomial-time reduction → method for solving one problem using another

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Important terminology

problem polynomial-time reduction reductions complexity problems many-one complete algorithm one exists class second first np classes polynomial may displaystyle turing

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Polynomial-time reductionis amethod for solving one problem using another0.90text
Linstance offor complexity classes within P0.80text
NLinstance offor complexity classes within P0.80text
NCinstance offor complexity classes within P0.80text
and P itselfinstance offor complexity classes within P0.80text
polynomial-time reductions cannot be used to define complete languagesinstance offor complexity classes within P0.80text
log-space reductions or NC reductions are used for defining classes of complete problems for these classesinstance ofweaker reductions0.80text
such as the P-complete problemsinstance ofweaker reductions0.80text
determining the rectilinear crossing number of an undirected graphinstance ofit has several other complete problems0.80text
Polynomial-time reductionrelated to CompletenessFor0.60section
Polynomial-time reductionrelated to CompletenessNP-complete0.60section
Polynomial-time reductionrelated to CompletenessNP0.60section

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