The impact of Entropy and Solution Density on selected SAT heuristics

In a recent article [Oh'15], Oh examined the impact of various key heuristics (e.g., deletion strategy, restart policy, decay factor, database reduction) in competitive SAT solvers. His key findings are that their expected success depends on whether the input formula is satisfiable or not. To further investigate these findings, we focused on two properties of satisfiable formulas: the entropy of the formula, which approximates the freedom we have in assigning the variables, and the solution density, which is the number of solutions divided by the search space. We found that both predict better the effect of these heuristics, and that satisfiable formulas with small entropy `behave' similarly to unsatisfiable formulas

Solving satisfiability problems by fluctuations: The dynamics of stochastic local search algorithms

Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random satisfiability problems. We find two different dynamical regimes, depending on the number of constraints per variable: For low constraintness, the problems are solved efficiently, i.e. in linear time. For higher constraintness, the solution times become exponential. We observe that the dynamical behavior is characterized by a fast equilibration and fluctuations around this equilibrium. If the algorithm runs long enough, an exponentially rare fluctuation towards a solution appears.Comment: 21 pages, 18 figures, revised version, to app. in PRE (2003

Minimizing energy below the glass thresholds

Focusing on the optimization version of the random K-satisfiability problem, the MAX-K-SAT problem, we study the performance of the finite energy version of the Survey Propagation (SP) algorithm. We show that a simple (linear time) backtrack decimation strategy is sufficient to reach configurations well below the lower bound for the dynamic threshold energy and very close to the analytic prediction for the optimal ground states. A comparative numerical study on one of the most efficient local search procedures is also given.Comment: 12 pages, submitted to Phys. Rev. E, accepted for publicatio

Effect of Initial Assignment on Local Search Performance for Max Sat

In this paper, we explore the correlation between the quality of initial assignments provided to local search heuristics and that of the corresponding final assignments. We restrict our attention to the Max r-Sat problem and to one of the leading local search heuristics - Configuration Checking Local Search (CCLS). We use a tailored version of the Method of Conditional Expectations (MOCE) to generate initial assignments of diverse quality. We show that the correlation in question is significant and long-lasting. Namely, even when we delve deeper into the local search, we are still in the shadow of the initial assignment. Thus, under practical time constraints, the quality of the initial assignment is crucial to the performance of local search heuristics. To demonstrate our point, we improve CCLS by combining it with MOCE. Instead of starting CCLS from random initial assignments, we start it from excellent initial assignments, provided by MOCE. Indeed, it turns out that this kind of initialization provides a significant improvement of this state-of-the-art solver. This improvement becomes more and more significant as the instance grows