How to Classify Hard and Soft Constraints in Non-binary Constraint Satisfaction Problems

2004 ◽  
pp. 213-226 ◽  
Author(s):  
Miguel A. Salido ◽  
Federico Barber
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Soft Constraints ◽  
Binary Constraint ◽  
Hard And Soft Constraints

STRONG DOMAIN FILTERING CONSISTENCIES FOR NON-BINARY CONSTRAINT SATISFACTION PROBLEMS

2008 ◽  
Vol 17 (05) ◽  
pp. 781-802 ◽  
Author(s):  
KOSTAS STERGIOU
Keyword(s):  
Empirical Study ◽  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Constraint Satisfaction Problems ◽  
Worst Case ◽  
Generic Algorithm ◽  
Binary Constraints ◽  
Binary Constraint

Domain filtering local consistencies, such as inverse consistencies, that only delete values and do not add new constraints are particularly useful in Constraint Programming. Although many such consistencies for binary constraints have been proposed and evaluated, the situation with non-binary constraints is quite different. Only very recently have domain filtering consistencies stronger than GAC started to attract interest. Following this line of research, we define a number of strong domain filtering consistencies for non-binary constraints and theoretically compare their pruning power. We prove that three of these consistencies are equivalent to maxRPC in binary CSPs while another is equivalent to PIC. We also describe a generic algorithm for domain filtering consistencies in non-binary CSPs. We show how this algorithm can be instantiated to enforce some of the proposed consistencies and analyze the worst-case complexities of the resulting algorithms. Finally, we make a preliminary empirical study.

scholarly journals Graph Neural Networks for Maximum Constraint Satisfaction

2021 ◽  
Vol 3 ◽  
Author(s):  
Jan Tönshoff ◽  
Martin Ritzert ◽  
Hinrikus Wolf ◽  
Martin Grohe
Keyword(s):  
Constraint Satisfaction ◽  
Network Architecture ◽  
Optimization Problems ◽  
Independent Set ◽  
Constraint Satisfaction Problems ◽  
Maximum Independent Set ◽  
Combinatorial Optimization Problems ◽  
Maximum Cut ◽  
Binary Constraint ◽  
Graph Neural Networks

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for all binary constraint satisfaction problems. Training is unsupervised, and it is sufficient to train on relatively small instances; the resulting networks perform well on much larger instances (at least 10-times larger). We experimentally evaluate our approach for a variety of problems, including Maximum Cut and Maximum Independent Set. Despite being generic, we show that our approach matches or surpasses most greedy and semi-definite programming based algorithms and sometimes even outperforms state-of-the-art heuristics for the specific problems.

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