The backtracking survey propagation algorithm for solving random K-SAT problems
This addresses the problem of efficiently solving large-scale combinatorial optimization problems for researchers in computer science and related fields, though it is incremental as it builds on existing survey propagation methods.
The authors tackled the challenge of solving hard random K-SAT problems near the SAT-UNSAT threshold by developing the backtracking survey propagation algorithm, which finds solutions in practically linear time in regions unreachable by other methods, with no frozen variables in the solutions.
Discrete combinatorial optimization has a central role in many scientific disciplines, however, for hard problems we lack linear time algorithms that would allow us to solve very large instances. Moreover, it is still unclear what are the key features that make a discrete combinatorial optimization problem hard to solve. Here we study random K-satisfiability problems with $K=3,4$, which are known to be very hard close to the SAT-UNSAT threshold, where problems stop having solutions. We show that the backtracking survey propagation algorithm, in a time practically linear in the problem size, is able to find solutions very close to the threshold, in a region unreachable by any other algorithm. All solutions found have no frozen variables, thus supporting the conjecture that only unfrozen solutions can be found in linear time, and that a problem becomes impossible to solve in linear time when all solutions contain frozen variables.