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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| Published in: | Journal of computer and system sciences Vol. 79; no. 1; pp. 144 - 151 |
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| Abstract | 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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| AbstractList | 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. We prove that weighted circuit satisfiability for monotone or antimonotone circuits has no fixed-parameter tractable approximation algorithm with any approximation ratio function I, unless FPT aNB W [ 1 ] . In particular, not having such an fpt-approximation algorithm implies that these problems have no polynomial-time approximation algorithms with ratio I (OPT) for any nontrivial function I. |
| Author | Marx, Dániel |
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| Cites_doi | 10.1007/BF01271272 10.1145/1993636.1993699 10.1137/06066850X 10.1145/1993636.1993698 10.1137/05064299X 10.1093/comjnl/bxm048 10.1145/210332.210337 10.1016/j.ipl.2008.09.017 10.1016/j.tcs.2008.09.065 10.1007/s00453-008-9223-x 10.1016/j.ipl.2009.07.016 10.1007/978-1-4612-0515-9 10.1007/978-3-540-73420-8_33 10.1109/CCC.2008.24 |
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| Keywords | Circuit satisfiability Circuits Fixed-parameter tractability Inapproximability |
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| Snippet | We prove that weighted circuit satisfiability for monotone or antimonotone circuits has no fixed-parameter tractable approximation algorithm with any... |
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| SubjectTerms | Algorithms Approximation Circuit satisfiability Circuits Fixed-parameter tractability Inapproximability Mathematical analysis Mathematical models |
| Title | Completely inapproximable monotone and antimonotone parameterized problems |
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