# The Potential of Restarts for ProbSAT

## TL;DR

This paper investigates the effectiveness of restart strategies for probSAT on near phase transition 3-SAT instances, demonstrating potential speedups and proposing a machine learning approach to optimize restart times.

## Contribution

It introduces a machine learning pipeline to determine optimal restart times for probSAT, significantly improving its performance over existing strategies.

## Key findings

- Potential speedup factor of 1.39 from empirical data
- Weibull distribution fits runtime data for over 93% of instances
- ProbSAT outperforms Luby's restart strategy with the proposed approach

## Abstract

This work analyses the potential of restarts for probSAT, a quite successful algorithm for k-SAT, by estimating its runtime distributions on random 3-SAT instances that are close to the phase transition. We estimate an optimal restart time from empirical data, reaching a potential speedup factor of 1.39. Calculating restart times from fitted probability distributions reduces this factor to a maximum of 1.30. A spin-off result is that the Weibull distribution approximates the runtime distribution for over 93% of the used instances well. A machine learning pipeline is presented to compute a restart time for a fixed-cutoff strategy to exploit this potential. The main components of the pipeline are a random forest for determining the distribution type and a neural network for the distribution's parameters. ProbSAT performs statistically significantly better than Luby's restart strategy and the policy without restarts when using the presented approach. The structure is particularly advantageous on hard problems.