Max 2-SAT
A classic optimization problem in theoretical computer science: given a 2-CNF formula, find an assignment that satisfies the maximum number of clauses simultaneously.
Timeline (last 90 days)
The paper proposes a class of deterministic polynomial-space algorithms for exactly solving the Max 2-SAT problem.
The new algorithm achieves a strict exponential speedup on several instance classes, reducing the total running time to O*(2^{(1-γ)n}), where γ>0 is a fixed constant.
The classical DPLL algorithm solves SAT problems through branching and unit propagation; a naive extension to Max 2-SAT traverses the full binary search tree and in the worst case needs to check 2^n assignments.
For semi-random 2-CNF formulas, the new algorithm remains exact and completes in O*(2^{(1-γ)n}) time with high probability.
To the authors' knowledge, this is the first polynomial-space algorithm with such a running time for a non-trivial dense class of Max 2-SAT instances.
A Max-Cut instance on each graph can be naturally transformed into a Max 2-SAT instance, where each edge corresponds to a clause requiring the two endpoints to belong to different parts.
The idea of pruning constraints can be added to any branching algorithm for Max 2-SAT.
All Facts (7)
The paper proposes a class of deterministic polynomial-space algorithms for exactly solving the Max 2-SAT problem.
50%UnverifiedThe new algorithm achieves a strict exponential speedup on several instance classes, reducing the total running time to O*(2^{(1-γ)n}), where γ>0 is a fixed constant.
50%UnverifiedThe classical DPLL algorithm solves SAT problems through branching and unit propagation; a naive extension to Max 2-SAT traverses the full binary search tree and in the worst case needs to check 2^n assignments.
50%UnverifiedFor semi-random 2-CNF formulas, the new algorithm remains exact and completes in O*(2^{(1-γ)n}) time with high probability.
50%UnverifiedTo the authors' knowledge, this is the first polynomial-space algorithm with such a running time for a non-trivial dense class of Max 2-SAT instances.
50%UnverifiedA Max-Cut instance on each graph can be naturally transformed into a Max 2-SAT instance, where each edge corresponds to a clause requiring the two endpoints to belong to different parts.
50%UnverifiedThe idea of pruning constraints can be added to any branching algorithm for Max 2-SAT.
50%