New methods for 3-SAT decision and worst-case analysis
Theoretical Computer Science
New upper bounds for maximum satisfiability
Journal of Algorithms
Upper Bounds for MaxSat: Further Improved
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT
Discrete Applied Mathematics - The renesse issue on satisfiability
Exact algorithms for finding minimum transversals in rank-3 hypergraphs
Journal of Algorithms
A new approach to proving upper bounds for MAX-2-SAT
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A new algorithm for optimal 2-constraint satisfaction and its implications
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Quasiconvex analysis of multivariate recurrence equations for backtracking algorithms
ACM Transactions on Algorithms (TALG)
A New Upper Bound for Max-2-SAT: A Graph-Theoretic Approach
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Optimal 2-constraint satisfaction via sum--product algorithms
Information Processing Letters
3-coloring in time O (1.3289n)
Journal of Algorithms
Feedback vertex set in mixed graphs
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Algorithms based on the treewidth of sparse graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Linear-programming design and analysis of fast algorithms for Max 2-CSP
Discrete Optimization
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In this paper we introduce ''hybrid'' Max 2-CSP formulas consisting of ''simple clauses'', namely conjunctions and disjunctions of pairs of variables, and general 2-variable clauses, which can be any integer-valued functions of pairs of boolean variables. This allows an algorithm to use both efficient reductions specific to AND and OR clauses, and other powerful reductions that require the general CSP setting. We use new reductions introduced here, and recent reductions such as ''clause-learning'' and ''2-reductions'' generalized to our setting@?s mixture of simple and general clauses. We parametrize a hybrid instance by the fraction p of non-simple clauses. We give an exact, exponential-time but polynomial-space algorithm that is the fastest known for p=0, which includes the well-studied Max 2-Sat problem but also instances with arbitrary mixtures of AND and OR clauses; for an m-clause instance it runs in time O^@?(2^m^/^6^.^3^2^1). The same algorithm is tied for fastest for general Max 2-CSP (p=1), with running time O^@?(2^m^/^5^.^2^6^3). The algorithm is the only one to treat mixtures of AND, OR, and general integer-valued clauses more efficiently than the general case, with intermediate running time bounds depending on the value of p. Since even a pure Max 2-Sat input instance may be transformed to a hybrid instance in the course of solving it, the algorithm@?s efficiency and generality go hand in hand. Our algorithm analysis and optimization use the familiar measure-and-conquer approach, but in a variation resulting in mathematical programs that are convex rather than quasi-convex, and can be solved efficiently and with a certificate of optimality. We produce a family of running-time upper-bound formulas, each optimized for instances with a particular value of p but valid for all instances.