ArticleNature communications2018
A continuous-time MaxSAT solver with high analog performance.
Article in Nature communications, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Bifurcation behaviors shape how continuous physical dynamics solves discrete Ising optimization.Nature communications · 2023Article
- Physics successfully implements Lagrange multiplier optimization.Proceedings of the National Academy of Sciences of the United States of America · 2020Article
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5 authors.
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Abstract
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.
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