2012 IEEE 27th Conference on Computational Complexity (2008)
June 22, 2008 to June 26, 2008
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2008.24
We prove that the weighted monotone circuit satisfiability problem has no fixed-parameter tractable approximation algorithm with constant or polylogarithmic approximation ratio unless FPT = W[P]. Our result answers a question of Alekhnovich and Razborov, who proved that the weighted monotone circuit satisfiability problem has no fixed-parameter tractable 2-approximation algorithm unless every problem in W[P] can be solved by a randomized fpt algorithm and asked whether their result can be derandomized. Alekhnovich and Razborov used their inapproximability result as a lemma for proving that resolution is not automatizable unless W[P] is contained in randomized FPT. It is an immediate consequence of our result that the complexity theoretic assumption can be weakened to W[P] =!= FPT. The decision version of the monotone circuit satisfiability problem is known to be complete for the class W[P]. By reducing them to the monotone circuit satisfiability problem with suitable approximation preserving reductions, we prove similar inapproximability results for all other natural minimisation problems known to be W[P]-complete.
parameterized complexity, inapproximability, derandomisation
Martin Grohe, Kord Eickmeyer, Magdalena Gr?, "Approximation of Natural W[P]-Complete Minimisation Problems Is Hard", 2012 IEEE 27th Conference on Computational Complexity, vol. 00, no. , pp. 8-18, 2008, doi:10.1109/CCC.2008.24