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A new upper bound for Max2SAT: A graphtheoretic approach
 In Mathematical Foundations of Computer Science (MFCS 2008
, 2008
"... Abstract. In MaxSat, we ask for an assignment which satisfies the maximum number of clauses for a boolean formula in CNF. We present an algorithm yielding a run time upper bound of O ∗ (2 1 6.2158 K) for Max2Sat (each clause contains at most 2 literals), where K is the number of clauses. The run t ..."
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Abstract. In MaxSat, we ask for an assignment which satisfies the maximum number of clauses for a boolean formula in CNF. We present an algorithm yielding a run time upper bound of O ∗ (2 1 6.2158 K) for Max2Sat (each clause contains at most 2 literals), where K is the number of clauses. The run time has been achieved by using heuristic priorities on the choice of the variable on which we branch. The implementation of these heuristic priorities is rather simple, though they have a significant effect on the run time. The analysis is done using a tailored nonstandard measure. 1
On the complexity of global constraint satisfaction
 In ISAAC’05
, 2005
"... We study the computational complexity of decision and optimization problems that may be expressed as boolean contraint satisfaction problem with the global cardinality constraints. In this paper we establish a characterization theorem for the decision problems and derive approximation hardness resul ..."
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We study the computational complexity of decision and optimization problems that may be expressed as boolean contraint satisfaction problem with the global cardinality constraints. In this paper we establish a characterization theorem for the decision problems and derive approximation hardness results for the corresponding global optimization problems. 1
Adding cardinality constraints to integer . . .
, 2007
"... MaxSATCC is the following optimization problem: Given a formula in CNF and a bound k, find an assignment with at most k variables being set to true that maximizes the number of satisfied clauses among all such assignments. If each clause is restricted to have at most ℓ literals, we obtain the prob ..."
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MaxSATCC is the following optimization problem: Given a formula in CNF and a bound k, find an assignment with at most k variables being set to true that maximizes the number of satisfied clauses among all such assignments. If each clause is restricted to have at most ℓ literals, we obtain the problem MaxℓSATCC. Sviridenko (Algorithmica, 30(3):398–405, 2001) designed a (1 − e −1)approximation algorithm for MaxSATCC. This result is tight unless P = NP (Feige, J. ACM, 45(4):634–652, 1998). Sviridenko asked if it is possible to achieve a better approximation ratio in the case of MaxℓSATCC. We answer this question in the affirmative by presenting a randomized approximation algorithm whose approximation ratio is 1−(1 − 1 ℓ)ℓ −ε. To do this, we develop a general technique for adding a cardinality constraint to certain integer programs. Our algorithm can be derandomized using pairwise independent random variables with small probability space.