New methods for 3-SAT decision and worst-case analysis
Theoretical Computer Science
New upper bounds for maximum satisfiability
Journal of Algorithms
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)
Optimal 2-constraint satisfaction via sum-product algorithms
Information Processing Letters
Quasiconvex analysis of multivariate recurrence equations for backtracking algorithms
ACM Transactions on Algorithms (TALG)
Measure and conquer: domination – a case study
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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
New bounds for MAX-SAT by clause learning
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
A new upper bound for Max-2-SAT: A graph-theoretic approach
Journal of Discrete Algorithms
Exact algorithms for dominating set
Discrete Applied Mathematics
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between
Journal of Computer and System Sciences
A faster algorithm for dominating set analyzed by the potential method
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
New upper bounds for MAX-2-SAT and MAX-2-CSP w.r.t. the average variable degree
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
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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. Parametrizing an instance by the fraction p of nonsimple clauses, we give an exact (exponential-time) algorithm that is the fastest polynomial-space algorithm known for Max 2-Sat (and other p = 0 formulas, with arbitrary mixtures of AND and OR clauses); the only efficient algorithm for mixtures of AND, OR, and general integer-valued clauses; and tied for fastest for general Max 2-CSP (p = 1). Since a pure 2-Sat input instance may be transformed to a general CSP instance in the course of being solved, the algorithm's efficiency and generality go hand in hand. Our novel analysis results in a family of running-time bounds, each optimized for a particular value of p. The algorithm uses new reductions introduced here, as well as recent reductions such as "clause-learning" and "2-reductions" adapted to our setting's mixture of simple and general clauses. Each reduction imposes constraints on various parameters, and the running-time bound is an "objective function" of these parameters and p. The optimal running-time bound is obtained by solving a convex nonlinear program, which can be done efficiently and with a certificate of optimality.