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APX

In computational complexity theory, the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short). In simple terms, problems in this class have efficient algorithms that can…

APX-hardness and APX-completeness, Definition & Related complexity classes

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Definition

APX-hardness and APX-completeness

Related complexity classes

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APX

Nodes29
Edges28
Triples62
Avg. degree1.93
Density0.068966
Components1

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APX

Top relations

related to References · 17
APX → APXC, Archived, Complexity Zoo, Computer, Gerhard Woeginger, Journal, Magnús Halldórsson, Marek Karpinski, Maximum Satisfiability Archived, NP, Optimization, Papadimitriou, Pierluigi Crescenzi, System Sciences, Viggo Kann, Wayback Machine, Yannakakis
related to APX-intermediate · 10
APX → APX-complete, APX-hard, APX-intermediate, Despite, NP, One, PTAS, Such, The, Unless
related to Definition · 10
APX → An, For, Here, In, NP, One, Problems, PTAS, The, Unless
related to f(n)-APX · 9
APX → AP-reductions, APX-complete, APX-completeness, Log-APX, Log-APX-complete, Log-APX-completeness, One, Poly-APX, PTAS-reductions
related to APX-hardness and APX-completeness · 8
APX → APX-complete, APX-completeness, APX-hard, As, In, L-reductions, NP, PTAS
related to Examples · 6
APX → APX-complete, Boolean, In, MAX-3SAT, One, Other APX-complete
related to PTAS · 2
APX → PTAS, This

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Important terminology

problems approximation problem ptas set ratio factor displaystyle within class complexity algorithms np one classes input size apx-complete min optimization

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
APXrelated to APX-hardness and APX-completenessAPX-hard0.60section
APXrelated to APX-hardness and APX-completenessPTAS0.60section
APXrelated to APX-hardness and APX-completenessAPX-complete0.60section
APXrelated to APX-hardness and APX-completenessAs0.60section
APXrelated to APX-hardness and APX-completenessNP0.60section
APXrelated to APX-hardness and APX-completenessIn0.60section
APXrelated to APX-hardness and APX-completenessAPX-completeness0.60section
APXrelated to APX-hardness and APX-completenessL-reductions0.60section
APXrelated to APX-intermediateUnless0.60section
APXrelated to APX-intermediateNP0.60section
APXrelated to APX-intermediatePTAS0.60section
APXrelated to APX-intermediateAPX-complete0.60section

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