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)
Exact Max 2-Sat: Easier and Faster
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice 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
MAX-SAT for formulas with constant clause density can be solved faster than in O(2n) time
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
An exact algorithm for MAX-CUT in sparse graphs
Operations Research Letters
Linear-programming design and analysis of fast algorithms for Max 2-CSP
Discrete Optimization
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MAX-2-SAT and MAX-2-CSP are important NP-hard optimization problems generalizing many graph problems. Despite many efforts, the only known algorithm (due to Williams) solving them in less than 2n steps uses exponential space. Scott and Sorkin give an algorithm with 2n(1 - 2/{d+1}) time and polynomial space for these problems, where d is the average variable degree. We improve this bound to O*(2n(1- {10/3}/{d+1})) for MAX-2-SAT and O*(2n(1- 3/{d+1})) for MAX-2-CSP. We also prove stronger upper bounds for d bounded from below. E.g., for d≥10 the bounds improve to O*(2n(1- {3.469}/{d+1})) and O*(2n(1- {3.221}/{d+1})), respectively. As a byproduct we get a simple proof of an O*(2m/5.263) upper bound for MAX-2-CSP, where m is the number of constraints. This matches the best known upper bound w.r.t. m due to Gaspers and Sorkin.