Max 2-SAT with up to 108 qubits

Random Max 2-sat and Max Cut

Given a 2-SAT formula F consisting of n variables and b n random clauses, what is the largest number of clauses maxF satisfiable by a single assignment of the variables? We bound the answer away from the trivial bounds of 34 n and n. We prove that for < 1, the expected number of clauses satisfiable is b n o(1); for large , it is ( 34 + (p ))n; for = 1 + ", it is at least (1 + " O("3))n and at m...

Improved Branch and Bound Algorithms for Max-2-SAT and Weighted Max-2-SAT

We present novel branch and bound algorithms for solving Max-SAT and weighted Max-SAT, and provide experimental evidence that outperform the algorithm of Borchers & Furman on Max-2-SAT and weighted Max-2-SAT instances. Our algorithms decrease the time needed to solve an instance, as well as the number of backtracks, up to two orders of magnitude.

New Worst-Case Upper Bounds for MAX-2-SAT with Application to MAX-CUT

Tight Bounds For Random MAX 2-SAT

For a conjunctive normal form formula F with n variables and m = cn 2-variable clauses (c is called the density), denote by maxF is the maximum number of clauses satisfiable by a single assignment of the variables. For the uniform random formula F with density c = 1 + ε, ε À n−1/3, we prove that maxF is in (1 + ε−Θ(ε3))n with high probability. This improves the known upper bound (1 + ε − Ω(ε3/ ...

Exact Max 2-Sat: Easier and Faster

Prior algorithms known for exactly solving Max 2-Sat improve upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted Max 2-Sat instances. One of them has a good performance if the underlying constraint graph has a small separator decomposition, another has a slightly improved worst case performance. For a 2-Sat inst...