Completely inapproximable monotone and antimonotone parameterized problems

We prove that weighted circuit satisfiability for monotone or antimonotone circuits has no fixed-parameter tractable approximation algorithm with any approximation ratio function ρ, unless FPT≠W[1]. In particular, not having such an fpt-approximation algorithm implies that these problems have no pol...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 79; no. 1; pp. 144 - 151
Main Author: Marx, Dániel
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2013
Subjects:
Algorithms
Approximation
Circuit satisfiability
Circuits
Fixed-parameter tractability
Inapproximability
Mathematical analysis
Mathematical models
Circuit satisfiability
Circuits
Fixed-parameter tractability
Inapproximability
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:We prove that weighted circuit satisfiability for monotone or antimonotone circuits has no fixed-parameter tractable approximation algorithm with any approximation ratio function ρ, unless FPT≠W[1]. In particular, not having such an fpt-approximation algorithm implies that these problems have no polynomial-time approximation algorithms with ratio ρ(OPT) for any nontrivial function ρ. ► We show fpt-inapproximability results for natural problems. ► Results are under the standard complexity assumption that FPT is different from W[1]. ► Weighted Monotone Circuit Satisfiability has no fpt-approximation for any ratio. ► Weighted Antimonotone Circuit Satisfiability has no fpt-approximation for any ratio.
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ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2012.09.001