Local equations describe unreasonably efficient stochastic algorithms in random K-SAT Article Swipe
David Machado
,
Jonathan González-García
,
Roberto Mulet
,
David Machado
,
Jonathan González-García
,
Roberto Mulet
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1073/pnas.2510153122
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1073/pnas.2510153122
Despite significant advances in characterizing the highly nonconvex landscapes of constraint satisfaction problems, the good performance of certain algorithms in solving hard combinatorial optimization tasks remains poorly understood. This gap in understanding stems largely from the lack of theoretical tools for analyzing their out-of-equilibrium dynamics. To address this challenge, we develop a system of approximate master equations that capture the behavior of local search algorithms in constraint satisfaction problems. Our framework shows excellent qualitative agreement with the phase diagrams of two paradigmatic algorithms: Focused Metropolis Search (FMS) and greedy-WalkSAT (G-WalkSAT) for random 3-SAT. The equations not only confirm the numerical observation that G-WalkSAT’s algorithmic threshold is nearly parameter-independent but also successfully predict FMS’s threshold beyond the clustering transition. We also exploit these equations in a decimation scheme, demonstrating that the computed marginals encode valuable information about the local structure of the solution space explored by stochastic algorithms. Notably, our decimation approach achieves a threshold that surpasses the clustering transition, outperforming conventional methods like Belief Propagation-guided decimation. These results challenge the prevailing assumption that long-range correlations are always necessary to describe efficient local search dynamics and open a path to designing efficient algorithms to solve combinatorial optimization problems.
Related Topics
Concepts
Local search (optimization)
Cluster analysis
Decimation
Mathematical optimization
Constraint (computer-aided design)
Algorithm
Constraint satisfaction problem
Computer science
Path (computing)
Exploit
Mathematics
Constraint satisfaction
ENCODE
Theoretical computer science
Vertex (graph theory)
Optimization problem
Search algorithm
Space (punctuation)
Combinatorial optimization
Minification
Stochastic process
Coherence (philosophical gambling strategy)
Computational complexity theory
Hierarchical clustering
Local optimum
Local consistency
Stochastic optimization
Cluster (spacecraft)
Global optimization
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1073/pnas.2510153122
- OA Status
- hybrid
- References
- 38
- OpenAlex ID
- https://openalex.org/W7108739211
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W7108739211Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1073/pnas.2510153122Digital Object Identifier
- Title
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Local equations describe unreasonably efficient stochastic algorithms in random K-SATWork title
- Type
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articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2025Year of publication
- Publication date
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2025-12-05Full publication date if available
- Authors
-
David Machado, Jonathan González-García, Roberto Mulet, David Machado, Jonathan González-García, Roberto MuletList of authors in order
- Landing page
-
https://doi.org/10.1073/pnas.2510153122Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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hybridOpen access status per OpenAlex
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https://doi.org/10.1073/pnas.2510153122Direct OA link when available
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Local search (optimization), Cluster analysis, Decimation, Mathematical optimization, Constraint (computer-aided design), Algorithm, Constraint satisfaction problem, Computer science, Path (computing), Exploit, Mathematics, Constraint satisfaction, ENCODE, Theoretical computer science, Vertex (graph theory), Optimization problem, Search algorithm, Space (punctuation), Combinatorial optimization, Minification, Stochastic process, Coherence (philosophical gambling strategy), Computational complexity theory, Hierarchical clustering, Local optimum, Local consistency, Stochastic optimization, Cluster (spacecraft), Global optimizationTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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| abstract_inverted_index.dynamics. | 44 |
| abstract_inverted_index.efficient | 180, 190 |
| abstract_inverted_index.equations | 56, 94, 122 |
| abstract_inverted_index.excellent | 72 |
| abstract_inverted_index.framework | 70 |
| abstract_inverted_index.marginals | 131 |
| abstract_inverted_index.necessary | 177 |
| abstract_inverted_index.nonconvex | 7 |
| abstract_inverted_index.numerical | 99 |
| abstract_inverted_index.problems, | 12 |
| abstract_inverted_index.problems. | 68, 196 |
| abstract_inverted_index.structure | 138 |
| abstract_inverted_index.surpasses | 155 |
| abstract_inverted_index.threshold | 104, 113, 153 |
| abstract_inverted_index.Metropolis | 84 |
| abstract_inverted_index.algorithms | 18, 64, 191 |
| abstract_inverted_index.assumption | 171 |
| abstract_inverted_index.challenge, | 48 |
| abstract_inverted_index.clustering | 116, 157 |
| abstract_inverted_index.constraint | 10, 66 |
| abstract_inverted_index.decimation | 125, 149 |
| abstract_inverted_index.landscapes | 8 |
| abstract_inverted_index.long-range | 173 |
| abstract_inverted_index.prevailing | 170 |
| abstract_inverted_index.stochastic | 145 |
| abstract_inverted_index.(G-WalkSAT) | 89 |
| abstract_inverted_index.algorithmic | 103 |
| abstract_inverted_index.algorithms. | 146 |
| abstract_inverted_index.algorithms: | 82 |
| abstract_inverted_index.approximate | 54 |
| abstract_inverted_index.decimation. | 165 |
| abstract_inverted_index.information | 134 |
| abstract_inverted_index.observation | 100 |
| abstract_inverted_index.performance | 15 |
| abstract_inverted_index.qualitative | 73 |
| abstract_inverted_index.significant | 1 |
| abstract_inverted_index.theoretical | 38 |
| abstract_inverted_index.transition, | 158 |
| abstract_inverted_index.transition. | 117 |
| abstract_inverted_index.understood. | 27 |
| abstract_inverted_index.conventional | 160 |
| abstract_inverted_index.correlations | 174 |
| abstract_inverted_index.optimization | 23, 195 |
| abstract_inverted_index.paradigmatic | 81 |
| abstract_inverted_index.satisfaction | 11, 67 |
| abstract_inverted_index.successfully | 110 |
| abstract_inverted_index.G-WalkSAT’s | 102 |
| abstract_inverted_index.combinatorial | 22, 194 |
| abstract_inverted_index.demonstrating | 127 |
| abstract_inverted_index.outperforming | 159 |
| abstract_inverted_index.understanding | 31 |
| abstract_inverted_index.characterizing | 4 |
| abstract_inverted_index.greedy-WalkSAT | 88 |
| abstract_inverted_index.Propagation-guided | 164 |
| abstract_inverted_index.out-of-equilibrium | 43 |
| abstract_inverted_index.parameter-independent | 107 |
| cited_by_percentile_year | |
| countries_distinct_count | 5 |
| institutions_distinct_count | 6 |
| citation_normalized_percentile.value | 0.83680926 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |