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Phase transition for Local Search on planted SAT [article]

Andrei A. Bulatov, Evgeny S. Skvortsov
2008 arXiv   pre-print
In this paper we give an analysis of Local Search on random planted 3-CNF formulas.  ...  As a byproduct we also show that for any constant r there is g such that Local Search applied to a random (not necessarily planted) 3-CNF with clause-to-variable ratio r produces an assignment that satisfies  ...  In this paper we analyze the performance of one of the simplest algorithms for (MAX-)k-SAT, the Local Search algorithm, on random planted instances. The distribution.  ... 
arXiv:0811.2546v1 fatcat:cmw6zhbpnbds3i6fzqmigmd4zu

A Wealth of SAT Distributions with Planted Assignments [chapter]

Tassos Dimitriou
2003 Lecture Notes in Computer Science  
complexity for good assignments and a new type of phase transition which is related to the uniqueness of the optimal solution.  ...  First, we give a generator for instances of MAX k-SAT, the version of k-SAT where one wants to maximize the number of satisfied clauses.  ...  The use of distributions for generating random SAT instances is therefore an important set of benchmark problems for evaluating local search SAT heuristics.  ... 
doi:10.1007/978-3-540-45193-8_19 fatcat:tddfuduc4beunphbffhu7oyqmy

SAT distributions with planted assignments and phase transitions between decision and optimization problems

Tassos Dimitriou
2005 Discrete Applied Mathematics  
Furthermore, we demonstrate that these phase transitions are related to sudden changes to a quantity similar to the backbone of a SAT formula.  ...  Under the right choice of these parameters an easy-hard-easy pattern in the search complexity emerges which is similar to the patterns observed for traditional SAT distributions.  ...  Acknowledgements The author wishes to thank Christos Papadimitriou and the anonymous reviewers for some very useful comments.  ... 
doi:10.1016/j.dam.2005.05.006 fatcat:hud2d2j3fzhhphjkmh3f63o4ja

Reweighted Belief Propagation and Quiet Planting for Random K-SAT

Florent Krzakala, Marc Mézard, Lenka Zdeborová
2014 Journal on Satisfiability, Boolean Modeling and Computation  
We are hence able to generate at the same time a typical random SAT instance and one of its solutions.  ...  We exhibit, in some large planted instances, solutions with a non-trivial whitening core; such solutions were known to exist but were so far never found on very large instances.  ...  to be quite large, it includes the local search algorithms, as well as message-passing ones.  ... 
doi:10.3233/sat190096 fatcat:locashkltngn5cixxepvnxh6va

Backbone Analysis and Applications in Heuristic Algorithm Design

He JIANG, Tie QIU, Yan HU, Ming-Chu LI, Zhong-Xuan LUO
2011 ACTA AUTOMATICA SINICA  
Configuration landscape analysis and backbone guided local search: Part I: satisfiability and maximum satisfiability.  ...  Fitness landscapes, memetic algorithms, and greedy operators for graph bipartitioning. Evolutionary Computation, 2000, 8(1): 61−91 47 Reeves C R. Landscapes, operators and heuristic search.  ...  SAT distributions with planted assignment sand phase transitions between decision and optimization problems. Discrete Applied Mathematics, 2005, 153(1): 58−72 12 Zhang W X.  ... 
doi:10.3724/sp.j.1004.2011.00257 fatcat:dbvrdmoqynaulcpwrfiruateq4

Reweighted belief propagation and quiet planting for random K-SAT [article]

Florent Krzakala and Marc Mézard and Lenka Zdeborová
2014 arXiv   pre-print
We are hence able to generate at the same time a typical random SAT instance and one of its solutions.  ...  We exhibit, in some large planted instances, solutions with a non-trivial whitening core; such solutions were known to exist but were so far never found on very large instances.  ...  to be quite large, it includes the local search algorithms, as well as message-passing ones.  ... 
arXiv:1203.5521v3 fatcat:pz6rmq2rlnhrteaworn6vvsxxq

SAT Distributions with Phase Transitions between Decision and Optimization Problems

Tassos Dimitriou
2003 Electronic Notes in Discrete Mathematics  
Furthermore, we demonstrate that these phase transitions are related to sudden changes to a quantity similar to the backbone of a SAT formula.  ...  Under the right choice of these parameters an easy-hard-easy pattern in the search complexity emerges which is similar to the patterns observed for traditional SAT distributions.  ...  Acknowledgements Many thanks to Christos Papadimitriou for some very useful comments.  ... 
doi:10.1016/s1571-0653(04)00459-7 fatcat:kaglvhdx7zaktbfbuj7jk33vn4

A New Method for 3-Satisfiability Problem Solving Space Structure on Structural Entropy

Chen Liang, Xiaofeng Wang, Lei Lu, Pengfei Niu
2021 Symmetry  
The analysis of different phase transition points and solution regions is based on different metric analysis models.  ...  The solution space of 3-SAT problem is obtained by planting strategy and belief propagation.  ...  Acknowledgments: We would like to thank the anonymous referees for their helpful comments and suggestions. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/sym13112005 fatcat:oludl3tu7jem5mkz74rv7hs42e

Multiple Sequence Alignment [chapter]

2005 Bioinformatics and Functional Genomics  
Multiple sequence alignment is a central problem in Bioinformatics and a challenging one for optimisation algorithms.  ...  Alignments obtained with a pseudo-Boolean local search algorithm are competitive with those of state-of-the-art algorithms.  ...  Similar constraints were found to improve local search performance on SAT-encoded clique problems [21] , and they also help on this model.  ... 
doi:10.1002/047145916x.ch10 fatcat:meduj3bui5grvhbvbjg4lwawju

From one solution of a 3-satisfiability formula to a solution cluster: Frozen variables and entropy

Kang Li, Hui Ma, Haijun Zhou
2009 Physical Review E  
A solution to a 3-satisfiability (3-SAT) formula can be expanded into a cluster, all other solutions of which are reachable from this one through a sequence of single-spin flips.  ...  From the calculated entropy values, we infer that, for a large random 3-SAT formula with constraint density close to the satisfiability threshold, the solutions obtained by the survey-propagation or the  ...  Cook, in Proceedings of the 3rd Annual ACM Symposium on Theory of Computing (1971), pp. 151-158.  ... 
doi:10.1103/physreve.79.031102 pmid:19391897 fatcat:vva7sv4a5jdyhikxzz7fzztuve

A review of the Statistical Mechanics approach to Random Optimization Problems [article]

Fabrizio Altarelli, Remi Monasson, Guilhem Semerjian, Francesco Zamponi
2008 arXiv   pre-print
We discuss and characterize the different phase transitions that are met in these problems, starting from basic concepts.  ...  We also discuss how statistical mechanics methods can be used to investigate the behavior of local search and decimation based algorithms.  ...  LOCAL SEARCH ALGORITHMS The following of this review will be devoted to the study of various solving algorithms for SAT formulas.  ... 
arXiv:0802.1829v1 fatcat:wv65adl4v5cmzjxon6unr7mg6q

Efficient solution of Boolean satisfiability problems with digital memcomputing

Sean R. B. Bearden, Yan Ru Pei, Massimiliano Di Ventra
2020 Scientific Reports  
scalability while solving "hard" planted-solution instances of SAT, known to require exponential time to solve in the typical case for both complete and incomplete algorithms.  ...  The efficiency of the simulations is related to the collective dynamical properties of the original physical system that persist in the numerical integration to robustly guide the solution search even  ...  The insets show exponential scalability for a stochastic local-search algorithm (WalkSAT) and a survey-inspired decimation procedure (SID) on the same instances. (S is for number of steps.)  ... 
doi:10.1038/s41598-020-76666-2 pmid:33184386 fatcat:atf7fwc3cze2rauquumzysfciy

Interdependent couplings map to thermal, higher-order interactions [article]

Ivan Bonamassa, Bnaya Gross, Shlomo Havlin
2021 arXiv   pre-print
Yet, physical realizations of this coupling are still unknown, due to the lack of a theoretical framework for their study.  ...  Finally, we discover an isomorphism between the ground state of random multi-spin models and interdependent percolation on randomly coupled networks.  ...  The OP, ψ, of the K-xor-sat freezing transition-called 1−t in Ref.  ... 
arXiv:2110.08907v1 fatcat:xuvuvvrwibd4bhnan4soifb3jy

Directed percolation and numerical stability of simulations of digital memcomputing machines [article]

Yuan-Hang Zhang, Massimiliano Di Ventra
2021 arXiv   pre-print
They can be physically realized with continuous-time, non-quantum dynamical systems with memory (time non-locality), whose ordinary differential equations (ODEs) can be numerically integrated on modern  ...  instances with planted solutions.  ...  -SAT instances with planted solutions.  ... 
arXiv:2102.03547v2 fatcat:74lpywiirraqxhy4nxl5wwrqr4

Phase transitions in semisupervised clustering of sparse networks

Pan Zhang, Cristopher Moore, Lenka Zdeborová
2014 Physical Review E  
A recently-discovered phase transition puts fundamental limits on the accuracy of these predictions if we have access only to the network topology.  ...  We study the phase diagram of this "semisupervised" learning problem for networks generated by the stochastic block model.  ...  We are grateful to Florent Krzakala, Elchanan Mossel, and Allan Sly for helpful conversations.  ... 
doi:10.1103/physreve.90.052802 pmid:25493829 fatcat:curlwacgkrdpjeehp4fdkrffbe
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