Locally Consistent Constraint Satisfaction Problems with Binary Constraints

2005 ◽  
pp. 295-306 ◽  
Author(s):  
Manuel Bodirsky ◽  
Daniel Král’
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Binary Constraints ◽  
Consistent Constraint

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 Locally consistent constraint satisfaction problems

2005 ◽  
Vol 348 (2-3) ◽  
pp. 187-206 ◽  
Author(s):  
Zdeněk Dvořák ◽  
Daniel Král’ ◽  
Ondřej Pangrác
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Consistent Constraint

scholarly journals Binary Encodings of Non-binary Constraint Satisfaction Problems: Algorithms and Experimental Results

2005 ◽  
Vol 24 ◽  
pp. 641-684 ◽  
Author(s):  
N. Samaras ◽  
K. Stergiou
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Binary Representation ◽  
Binary Constraints ◽  
Arc Consistency ◽  
Binary Problem ◽  
Binary Constraint ◽  
Binary Problems ◽  
Standard Techniques

A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally accepted that the translated problem can be solved by applying well-established techniques for binary CSPs. In this paper we evaluate the applicability of the latter approach. We demonstrate that the use of standard techniques for binary CSPs in the encodings of non-binary problems is problematic and results in models that are very rarely competitive with the non-binary representation. To overcome this, we propose specialized arc consistency and search algorithms for binary encodings, and we evaluate them theoretically and empirically. We consider three binary representations; the hidden variable encoding, the dual encoding, and the double encoding. Theoretical and empirical results show that, for certain classes of non-binary constraints, binary encodings are a competitive option, and in many cases, a better one than the non-binary representation.

scholarly journals Bipartite Encoding: A New Binary Encoding for Solving Non-Binary CSPs

2020 ◽  
Author(s):  
Ruiwei Wang ◽  
Roland H.C. Yap
Keyword(s):  
Constraint Satisfaction ◽  
State Of The Art ◽  
Constraint Satisfaction Problems ◽  
Special Structure ◽  
Large Set ◽  
Hidden Variable ◽  
Binary Constraints ◽  
Arc Consistency ◽  
Binary Encoding

Constraint Satisfaction Problems (CSPs) are typically solved with Generalized Arc Consistency (GAC). A general CSP can also be encoded into a binary CSP and solved with Arc Consistency (AC). The well-known Hidden Variable Encoding (HVE) is still a state-of-the-art binary encoding for solving CSPs. We propose a new binary encoding, called Bipartite Encoding (BE) which uses the idea of partitioning constraints. A BE encoded CSP can achieve a higher level of consistency than GAC on the original CSP. We give an algorithm for creating compact bipartite encoding for non-binary CSPs. We present a AC propagator on the binary constraints from BE exploiting their special structure. Experiments on a large set of non-binary CSP benchmarks with table constraints using the Wdeg, Activity and Impact heuristics show that BE with our AC propagator can outperform existing state-of-the-art GAC algorithms (CT, STRbit) and binary encodings (HVE with HTAC).

scholarly journals Random Subcubes as a Toy Model for Constraint Satisfaction Problems

2008 ◽  
Vol 131 (6) ◽  
pp. 1121-1138 ◽  
Author(s):  
Thierry Mora ◽  
Lenka Zdeborová
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems
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