Rounding Meets Approximate Model Counting
This addresses a bottleneck in approximate model counting for applications requiring high confidence, offering a significant performance improvement over existing methods.
The paper tackles the scalability issue of hashing-based approximate model counting for high-confidence estimates by introducing a rounding-based approach, resulting in RoundMC solving 204 more instances and achieving a 4x speedup over the state-of-the-art ApproxMC on a benchmark of 1890 instances.
The problem of model counting, also known as #SAT, is to compute the number of models or satisfying assignments of a given Boolean formula $F$. Model counting is a fundamental problem in computer science with a wide range of applications. In recent years, there has been a growing interest in using hashing-based techniques for approximate model counting that provide $(\varepsilon, δ)$-guarantees: i.e., the count returned is within a $(1+\varepsilon)$-factor of the exact count with confidence at least $1-δ$. While hashing-based techniques attain reasonable scalability for large enough values of $δ$, their scalability is severely impacted for smaller values of $δ$, thereby preventing their adoption in application domains that require estimates with high confidence. The primary contribution of this paper is to address the Achilles heel of hashing-based techniques: we propose a novel approach based on rounding that allows us to achieve a significant reduction in runtime for smaller values of $δ$. The resulting counter, called RoundMC, achieves a substantial runtime performance improvement over the current state-of-the-art counter, ApproxMC. In particular, our extensive evaluation over a benchmark suite consisting of 1890 instances shows that RoundMC solves 204 more instances than ApproxMC, and achieves a $4\times$ speedup over ApproxMC.