A continuous-time MaxSAT solver with high analog performance

, , ,

Nature Communications, 9, 4864 (2018) .


Many real-life optimization problems can be formulated in Boolean logic as MaxSAT, a class of problems where the task is finding Boolean assignments to variables satisfying the maximum number of logical constraints. Since MaxSAT is NP-hard, no algorithm is known to efficiently solve these problems. Here we present a continuous-time analog solver for MaxSAT and show that the scaling of the escape rate, an invariant of the solver’s dynamics, can predict the maximum number of satisfiable constraints, often well before finding the optimal assignment. Simulating the solver, we illustrate its performance on MaxSAT competition problems, then apply it to two-color Ramsey number R(m, m) problems. Although it finds colorings without monochromatic 5-cliques of complete graphs on N ≤ 42 vertices, the best coloring for N = 43 has two monochromatic 5-cliques, supporting the conjecture that R(5, 5) = 43. This approach shows the potential of continuous-time analog dynamical systems as algorithms for discrete optimization.

Add your rating and review

If all scientific publications that you have read were ranked according to their scientific quality and importance from 0% (worst) to 100% (best), where would you place this publication? Please rate by selecting a range.

0% - 100%

This publication ranks between % and % of publications that I have read in terms of scientific quality and importance.

Keep my rating and review anonymous
Show publicly that I gave the rating and I wrote the review