Should Algorithms for Random SAT and Max-SAT be Different?
This addresses algorithm design challenges for random Max-SAT, a key problem in computational complexity and optimization, with incremental improvements in solver performance.
The paper analyzes differences between random SAT and Max-SAT problems, finding that for certain formula ratios, Max-SAT can be solved by SAT algorithms with subexponential slowdown, while for higher ratios, different heuristics are needed; it proposes ProMS, a novel probabilistic approach that outperforms state-of-the-art local search solvers on random Max-SAT benchmarks.
We analyze to what extent the random SAT and Max-SAT problems differ in their properties. Our findings suggest that for random $k$-CNF with ratio in a certain range, Max-SAT can be solved by any SAT algorithm with subexponential slowdown, while for formulae with ratios greater than some constant, algorithms under the random walk framework require substantially different heuristics. In light of these results, we propose a novel probabilistic approach for random Max-SAT called ProMS. Experimental results illustrate that ProMS outperforms many state-of-the-art local search solvers on random Max-SAT benchmarks.