Results 1  10
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15
MaxSolver: An efficient exact algorithm for (weighted) maximum satisfiability
 Artificial Intelligence
, 2005
"... Artificial Intelligence, to appear Maximum Boolean satisfiability (maxSAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a Boolean formula. A branch and bound algorithm based on the DavisPutnam ..."
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Cited by 32 (1 self)
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Artificial Intelligence, to appear Maximum Boolean satisfiability (maxSAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a Boolean formula. A branch and bound algorithm based on the DavisPutnamLogemannLoveland procedure (DPLL) is one of the most competitive exact algorithms for solving maxSAT. In this paper, we propose and investigate a number of strategies for maxSAT. The first strategy is a set of unit propagation or unit resolution rules for maxSAT. We summarize three existing unit propagation rules and propose a new one based on a nonlinear programming formulation of maxSAT. The second strategy is an effective lower bound based on linear programming (LP). We show that the LP lower bound can be made effective as the number of clauses increases. The third strategy consists of a a binaryclause first rule and a dynamicweighting variable ordering rule, which are motivated by a thorough analysis of two existing wellknown variable orderings. Based on the analysis of these strategies, we develop an exact solver for both maxSAT and weighted maxSAT. Our experimental results on random problem instances and many instances from the maxSAT libraries show that our new solver outperforms most of the existing exact maxSAT solvers, with orders of magnitude of improvement in many cases.
Detecting disjoint inconsistent subformulas for computing lower bounds for MaxSAT
 In AAAI Conference on Artificial Intelligence
, 2006
"... Many lower bound computation methods for branch and bound MaxSAT solvers can be explained as procedures that search for disjoint inconsistent subformulas in the MaxSAT instance under consideration. The difference among them is the technique used to detect inconsistencies. In this paper, we define ..."
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Cited by 31 (9 self)
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Many lower bound computation methods for branch and bound MaxSAT solvers can be explained as procedures that search for disjoint inconsistent subformulas in the MaxSAT instance under consideration. The difference among them is the technique used to detect inconsistencies. In this paper, we define five new lower bound computation methods: two of them are based on detecting inconsistencies via a unit propagation procedure that propagates unit clauses using an original ordering; the other three add an additional level of forward lookahead based on detecting failed literals. Finally, we provide empirical evidence that the new lower bounds are of better quality than the existing lower bounds, as well as that a solver with our new lower bounds greatly outperforms some of the best performing stateoftheart MaxSAT solvers on Max2SAT, Max3SAT, and MaxCut instances.
New inference rules for MaxSAT
 JAIR
, 2007
"... Abstract. Exact MaxSAT solvers, compared with SAT solvers, apply little inference at each node of the proof tree. Commonly used SAT inference rules like unit propagation produce a simplified formula that preserves satisfiability but, unfortunately, solving the MaxSAT problem for the simplified for ..."
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Cited by 26 (6 self)
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Abstract. Exact MaxSAT solvers, compared with SAT solvers, apply little inference at each node of the proof tree. Commonly used SAT inference rules like unit propagation produce a simplified formula that preserves satisfiability but, unfortunately, solving the MaxSAT problem for the simplified formula is not equivalent to solving it for the original formula. In this paper, we define a number of original inference rules that, besides being applied efficiently, transform MaxSAT instances into equivalent MaxSAT instances which are easier to solve. The soundness of the rules, that can be seen as refinements of unit resolution adapted to MaxSAT, are proved in a novel and simple way via an integer programming transformation. Aiming to find out how powerful the inference rules are in practice, we have developed a new MaxSAT solver, called MaxSatz, which incorporates those rules, and performed an experimental investigation. The results obtained provide empirical evidence that MaxSatz is very competitive and greatly outperforms the best stateoftheart MaxSAT solvers on random Max2SAT, random Max3SAT, MaxCut, and Graph 3coloring instances, as well as benchmarks submitted to the MaxSAT Evaluation 2006. 1
Improved exact solver for weighted maxsat
 In: Proc. of the 8th SAT conference. (2005
, 2005
"... Abstract. We present two new branch and bound weighted MaxSAT solvers (Lazy and Lazy ⋆ ) which incorporate original data structures and inference rules, and a lower bound of better quality. 1 ..."
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Cited by 20 (10 self)
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Abstract. We present two new branch and bound weighted MaxSAT solvers (Lazy and Lazy ⋆ ) which incorporate original data structures and inference rules, and a lower bound of better quality. 1
Exact Algorithms for MAXSAT
 In 4th Int. Workshop on First order Theorem Proving
, 2003
"... The maximum satisfiability problem (MAXSAT) is stated as follows: Given Boolean formula in CNF, find a truth assignment that satisfies the maximum possible number of its clauses. MAXSAT is MAXSNPcomplete and received much attention recently. One of the challenges posed by Alber, Gramm and Nieder ..."
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Cited by 18 (6 self)
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The maximum satisfiability problem (MAXSAT) is stated as follows: Given Boolean formula in CNF, find a truth assignment that satisfies the maximum possible number of its clauses. MAXSAT is MAXSNPcomplete and received much attention recently. One of the challenges posed by Alber, Gramm and Niedermeier in a recent survey paper asks: Can MAXSAT be solved in less than 2 ' "steps"? Here, n is the number of different variables in the formula and a step may take polynomial time of the input. We answered this challenge positively by showing that popular algorithm based on branchandbound is bounded by O(b2 ') in time, where b is the maximum number of occurrences of any variable in the input.
Improved Branch and Bound Algorithms for MAXSAT
, 2003
"... We present two new branch and bound algorithms for solving MaxSAT, and provide experimental evidence that outperform the algorithm of Borchers &Furman on randomly generated instances. Our approach decreases the time needed to solve an instance, as well as the number of backtracks, up to two ord ..."
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Cited by 18 (8 self)
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We present two new branch and bound algorithms for solving MaxSAT, and provide experimental evidence that outperform the algorithm of Borchers &Furman on randomly generated instances. Our approach decreases the time needed to solve an instance, as well as the number of backtracks, up to two orders of magnitude.
Improved exact algorithms for MAXSAT
 Discrete Applied Mathematics
, 2002
"... In this paper we present improved exact and parameterized algorithms for the maximum satisfiability problem. In particular, we give an algorithm that computes a truth assignment for a boolean formula F satisfying the maximum number of clauses in time O(1.3247 m F ), where m is the number of clause ..."
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Cited by 17 (1 self)
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In this paper we present improved exact and parameterized algorithms for the maximum satisfiability problem. In particular, we give an algorithm that computes a truth assignment for a boolean formula F satisfying the maximum number of clauses in time O(1.3247 m F ), where m is the number of clauses in F, and F  is the sum of the number of literals appearing in each clause in F. Moreover, given a parameter k, we give an O(1.3695 k + F ) parameterized algorithm that decides whether a truth assignment for F satisfying at least k clauses exists. Both algorithms improve the previous best algorithms by Bansal and Raman for the problem. Key words. maximum satisfiability, exact algorithms, parameterized algorithms. 1
Optimization Algorithms for the MinimumCost Satisfiability Problem
"... Given a Boolean satisfiability (Sat) problem whose variables have nonnegative weights, the minimumcost satisfiability (MinCostSat) problem finds a satisfying truth assignment that minimizes a weighted sum of the truth values of the variables. Many NPoptimization problems are either special cases ..."
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Cited by 17 (2 self)
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Given a Boolean satisfiability (Sat) problem whose variables have nonnegative weights, the minimumcost satisfiability (MinCostSat) problem finds a satisfying truth assignment that minimizes a weighted sum of the truth values of the variables. Many NPoptimization problems are either special cases of MinCostSat or can be transformed into MinCostSat efficiently. However, in the past, these problems have been largely considered in isolation. In this dissertation, we (1) classify existing MinCostSat problems, (2) study factors affecting the performance of MinCostSat solvers, (3) propose algorithms for MinCostSat problems, and (4) implement and validate the performance of stateoftheart solvers for special cases of MinCostSat, including set and binate covering, MaxSat, and grouppartial MaxSat. We categorize MinCostSat problems as either native or nonnative. Nonnative problems can only be transformed into MinCostSat by adding slack variables. These problems include the MaxSat, partial MaxSat, and grouppartial MaxSat problems which have applications ranging from course assignment to FPGA detailed routing. Native problems are various subcases of MinCostSat. We further divide these into two
New upper bounds for MaxSat
 Charles University, Praha, Faculty of Mathematics and Physics
, 1998
"... We describe exact algorithms that provide new upper bounds for the Maximum Satisfiability problem (MaxSat). We prove that MaxSat can be solved in time O(F  · 1.3972 K), where F  is the length of a formula F in conjunctive normal form and K is the number of clauses in F. We also prove the time b ..."
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Cited by 15 (5 self)
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We describe exact algorithms that provide new upper bounds for the Maximum Satisfiability problem (MaxSat). We prove that MaxSat can be solved in time O(F  · 1.3972 K), where F  is the length of a formula F in conjunctive normal form and K is the number of clauses in F. We also prove the time bounds O(F  · 1.3995 k), where k is the maximum number of satisfiable clauses, and O((1.1279) F  ) for the same problem. For Max2Sat this implies a bound of O(1.2722 K). An exponential time approximation algorithm by Dantsin et al. uses an exact algorithm for MaxSat as a building block and is therefore also improved.
Study of lower bound functions for max2sat
 In AAAI2004
, 2004
"... Recently, several lower bound functions are proposed for solving the MAX2SAT problem optimally in a branchandbound algorithm. These lower bounds improve significantly the performance of these algorithms. Based on the study of these lower bound functions, we propose a new, lineartime lower bound ..."
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Cited by 11 (0 self)
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Recently, several lower bound functions are proposed for solving the MAX2SAT problem optimally in a branchandbound algorithm. These lower bounds improve significantly the performance of these algorithms. Based on the study of these lower bound functions, we propose a new, lineartime lower bound function. We show that the new lower bound function is admissible and it is consistently and substantially better than other known lower bound functions. The result of this study is a highperformance implementation of an exact algorithm for MAX2SAT which outperforms any implementation of the same class.