A Simpler Exponential-Time Approximation Algorithm for MAX-\(k\)-SAT
Abstract
We present an extremely simple polynomial-space exponential-time \((1 - \varepsilon)\)-approximation algorithm for MAX-\(k\)-SAT that is (slightly) faster than the previous known polynomial-space \((1 - \varepsilon)\)-approximation algorithms by Hirsch (Discrete Applied Mathematics, 2003) and Escoffier, Paschos and Tourniaire (Theoretical Computer Science, 2014). Our algorithm repeatedly samples an assignment uniformly at random until finding an assignment that satisfies a large enough fraction of clauses. Surprisingly, we can show the efficiency of this simpler approach by proving that in any instance of MAX-\(k\)-SAT (or more generally any instance of MAXCSP), an exponential number of assignments satisfy a fraction of clauses close to the optimal value.
Fields of Study & Subjects
Constraint Satisfaction and Optimization
Formal Methods in Verification
Complexity and Algorithms in Graphs
Publication details
- Journal / source
- Society for Industrial and Applied Mathematics eBooks
- Publisher
- Society for Industrial and Applied Mathematics
- Pages
- 247–253
- Publication date
- 1 January 2026
- Language
- EN
- Document type
- Book chapter