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SODA
2010
ACM

Solving MAX-r-SAT Above a Tight Lower Bound

9 years 7 months ago
Solving MAX-r-SAT Above a Tight Lower Bound
We present an exact algorithm that decides, for every fixed r ≥ 2 in time O(m) + 2O(k2 ) whether a given multiset of m clauses of size r admits a truth assignment that satisfies at least ((2r − 1)m + k)/2r clauses. Thus Max-rSat is fixed-parameter tractable when parameterized by the number of satisfied clauses above the tight lower bound (1 − 2−r )m. This solves an open problem of Mahajan, Raman and Sikdar (J. Comput. System Sci., 75, 2009). Our algorithm is based on a polynomial-time data reduction procedure that reduces a problem instance to an equivalent algebraically represented problem with O(k2 ) variables. This is done by representing the instance as an appropriate polynomial, and by applying a probabilistic argument combined with some simple tools from Harmonic analysis to show that if the polynomial cannot be reduced to one of size O(k2 ), then there is a truth assignment satisfying the required number of clauses. We introduce a new notion of bikernelization from ...
Noga Alon, Gregory Gutin, Eun Jung Kim, Stefan Sze
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Where SODA
Authors Noga Alon, Gregory Gutin, Eun Jung Kim, Stefan Szeider, Anders Yeo
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