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The satisfiability threshold for randomly generated binary constraint satisfaction problems

Alan Frieze, Michael Molloy
2006 Random structures & algorithms (Print)  
We study two natural models of randomly generated constraint satisfaction problems.  ...  We determine how quickly the domain size must grow with n to ensure that these models are robust in the sense that they exhibit a non-trivial threshold of satisfiability, and we determine the asymptotic  ...  Introduction The Constraint Satisfaction Problem (CSP) is a broadly studied generalization of k-SAT.  ... 
doi:10.1002/rsa.20118 fatcat:zbvvznt7b5gt3musk2mjaupbf4

The Satisfiability Threshold for Randomly Generated Binary Constraint Satisfaction Problems [chapter]

Alan Frieze, Michael Molloy
2003 Lecture Notes in Computer Science  
We study two natural models of randomly generated constraint satisfaction problems.  ...  We determine how quickly the domain size must grow with n to ensure that these models are robust in the sense that they exhibit a non-trivial threshold of satisfiability, and we determine the asymptotic  ...  Introduction The Constraint Satisfaction Problem (CSP) is a broadly studied generalization of k-SAT.  ... 
doi:10.1007/978-3-540-45198-3_24 fatcat:uhvyu3miu5dspo277jnpe25jke

Page 7844 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews  
O.] (3-TRNT-C; Toronto, ON) A probabilistic analysis of randomly generated binary constraint satisfaction problems. Theoret. Comput. Sci. 290 (2003), no. 3, 1815-1828.  ...  Summary: “Solving non-binary constraint satisfaction problems, a crucial challenge today, can be tackled in two different ways: translating the non-binary problem into an equivalent binary one, or extending  ... 

NAIS: A Calibrated Immune Inspired Algorithm to Solve Binary Constraint Satisfaction Problems [chapter]

Marcos Zuñiga, María-Cristina Riff, Elizabeth Montero
2007 Lecture Notes in Computer Science  
The tests were carried out using random generated binary constraint satisfaction problems on the transition phase where are the hardest problems.  ...  We have calibrated our algorithm using Relevance Estimation and Value Calibration (REVAC), that is a new technique, recently introduced to find the parameter values for evolutionary algorithms.  ...  Binary Constraint Satisfaction Problems For simplicity we restrict our attention here to binary CSPs, where the constraints involve two variables. Binary constraints are binary relations.  ... 
doi:10.1007/978-3-540-73922-7_3 fatcat:lib3pdgiardshh5dt42shk6qcu

Random constraint satisfaction: Easy generation of hard (satisfiable) instances

Ke Xu, Frédéric Boussemart, Fred Hemery, Christophe Lecoutre
2007 Artificial Intelligence  
Li, Exact phase transitions in random constraint satisfaction problems, Journal of Artificial Intelligence Research 12 (2000) 93-103; K. Xu, W.  ...  In that case, a threshold point can be precisely located and all instances have the guarantee to be hard at the threshold, i.e., to have an exponential tree-resolution complexity.  ...  Acknowledgements We would like to thank the AIJ anonymous referees for their helpful comments and suggestions.  ... 
doi:10.1016/j.artint.2007.04.001 fatcat:ru3xqka5vff7rbn2tesiptyosm

Towards Effective Deep Learning for Constraint Satisfaction Problems [chapter]

Hong Xu, Sven Koenig, T. K. Satish Kumar
2018 Lecture Notes in Computer Science  
Many attempts have been made to apply machine learning techniques to constraint satisfaction problems (CSPs). However, none of them have made use of the recent advances in deep learning.  ...  To the best of our knowledge, this is the first effective application of deep learning to CSPs that yields >99.99% prediction accuracy on random Boolean binary CSPs whose constraint tightnesses or constraint  ...  The research at the University of Southern California (USC) was supported by National Science Foundation (NSF) under grant numbers 1724392, 1409987, and 1319966.  ... 
doi:10.1007/978-3-319-98334-9_38 fatcat:djqet76n4bf6jdqebtioh5ik4m

Stochastic Constraint Programming [article]

Toby Walsh
2009 arXiv   pre-print
They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability.  ...  To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming.  ...  If the fraction of the resulting constraint satisfaction problems that are satisfiable is at least equal to the threshold θ, then the original stochastic constraint satisfaction problem is likely to be  ... 
arXiv:0903.1152v1 fatcat:lyq6id4uefb6lojov435u3jcnm

Constraint satisfaction problems and neural networks: A statistical physics perspective

Marc Mézard, Thierry Mora
2009 Journal of Physiology - Paris  
On the other hand some crucial inference problems in neurobiology, like those generated in multi-electrode recordings, naturally translate into hard constraint satisfaction problems.  ...  In particular, the use of cutting edge statistical physics concepts and methods allow one to solve very large constraint satisfaction problems like random satisfiability, coloring, or error correction.  ...  Conclusion The message passing strategy often provides the most efficient algorithms for solving hard constraint satisfaction problems, or for inference in graphical models.  ... 
doi:10.1016/j.jphysparis.2009.05.013 pmid:19616623 fatcat:ajpvvpa3ujg5tgay6jpvrmh5z4

Constraint satisfaction problems and neural networks: a statistical physics perspective [article]

Marc Mezard, Thierry Mora
2008 arXiv   pre-print
On the other hand some crucial inference problems in neurobiology, like those generated in multi-electrode recordings, naturally translate into hard constraint satisfaction problems.  ...  In particular, the use of cutting edge statistical physics concepts and methods allow one to solve very large constraint satisfaction problems like random satisfiability, coloring, or error correction.  ...  Conclusion The message passing strategy often provides the most efficient algorithms for solving hard constraint satisfaction problems, or for inference in graphical models.  ... 
arXiv:0803.3061v1 fatcat:wadx7u6k6ralpgiypkimq4a2fu

Lossy Data Compression with Random Gates

Stefano Ciliberti, Marc Mézard, Riccardo Zecchina
2005 Physical Review Letters  
algorithm for constraint satisfaction problems derived from statistical physics.  ...  We introduce a new protocol for a lossy data compression algorithm which is based on constraint satisfaction gates.  ...  algorithm for constraint satisfaction problems derived from statistical physics.  ... 
doi:10.1103/physrevlett.95.038701 pmid:16090781 fatcat:expaem5gcjclzc6krbgt3yehiq

Towards the Patterns of Hard CSPs with Association Rule Mining [article]

Chendong Li
2009 arXiv   pre-print
The hardness of finite domain Constraint Satisfaction Problems (CSPs) is a very important research area in Constraint Programming (CP) community.  ...  patterns of the hardness of the randomly generated CSPs  ...  Constraint Satisfaction Problems A binary Constraint Satisfaction Problem (BCSP) is a CSP that satisfies the above (i) and (ii); the only difference is the constraint set C.  ... 
arXiv:0906.5040v1 fatcat:um5krrpvvbb6bm3kaudcfeh6cy

Sharp Thresholds for a Random Constraint Satisfaction Problem

Ya'nan Liu
2017 Open Journal of Applied Sciences  
The phenomenon of phase transition in constraint satisfaction problems (CSPs) plays a crucial role in the field of artificial intelligence and computational complexity theory.  ...  The randomly selected constraints constitute a random CSP instance. An assignment that satisfies all the constraints simultaneously is called a solution of the CSP instance.  ...  Many problems in the fields of artificial intelligence, computer science and automatic control can be modeled as constraint satisfaction problems.  ... 
doi:10.4236/ojapps.2017.710041 fatcat:kywg5uyedba5fpnagicr22l3uy

A heuristic incremental modeling approach to course timetabling [chapter]

Don Banks, Peter van Beek, Amnon Meisels
1998 Lecture Notes in Computer Science  
Speci cally, w e consider how a timetabling problem can be represented as a Constraint Satisfaction Problem (CSP), and propose an algorithm for its solution which i m p r o ves upon the basic idea of backtracking  ...  In this paper the application of constraint-based reasoning to timetable generation is examined.  ...  Satisfying all of the constraints does not guarantee 100% students satisfaction.  ... 
doi:10.1007/3-540-64575-6_37 fatcat:625wqwoq2bd3tg7lecd4s2kkiu

A self-adaptive differential evolution algorithm for binary CSPs

Hongjie Fu, Dantong Ouyang, Jiaming Xu
2011 Computers and Mathematics with Applications  
Attention is concentrated on varying F and CR dynamically with each generation evolution. SADE maintains the diversity of population and improves the global convergence ability.  ...  In order to balance an individual's exploration and exploitation capability for different evolving phases, F and CR are equal to two different self-adjusted nonlinear functions.  ...  We start with the necessary background on Constraint Satisfaction Problems and DE algorithms. In Section 3, we proposed SADE for binary CSPs.  ... 
doi:10.1016/j.camwa.2011.06.053 fatcat:5k4k2xfywrckxcknn4bapm4jfi

On the Behavior and Application of Constraint Weighting [chapter]

John Thornton, Abdul Sattar
1999 Lecture Notes in Computer Science  
We extend previous results from satisfiability testing by looking at the broader domain of constraint satisfaction and test for differences in performance using randomly generated problems and problems  ...  We find constraint weighting produces fairly consistent behaviour within problem domains, and is more influenced by the number and interconnectedness of constraints than the realism or randomness of a  ...  In addition we run tests on the well-studied problem of random binary constraint satisfaction [10] . For the purpose of the research, a university timetable problem generator was developed.  ... 
doi:10.1007/978-3-540-48085-3_32 fatcat:sedmnx3thvgirpbwa2lnp7anoy
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