scholarly journals Variable and value elimination in binary constraint satisfaction via forbidden patterns

2015 ◽  
Vol 81 (7) ◽  
pp. 1127-1143 ◽  
Author(s):  
David A. Cohen ◽  
Martin C. Cooper ◽  
Guillaume Escamocher ◽  
Stanislav Živný
Keyword(s):  
Constraint Satisfaction ◽  
Binary Constraint ◽  
Forbidden Patterns

scholarly journals Galois Connections for Patterns: An Algebra of Labelled Graphs

2021 ◽  
pp. 125-150
Author(s):  
David A. Cohen ◽  
Martin C. Cooper ◽  
Peter G. Jeavons ◽  
Stanislav Živný
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Galois Connection ◽  
Language Classes ◽  
Finite Set ◽  
Binary Constraint ◽  
Tree Width ◽  
To Come ◽  
Forbidden Patterns ◽  
Near Unanimity

AbstractA pattern is a generic instance of a binary constraint satisfaction problem (CSP) in which the compatibility of certain pairs of variable-value assignments may be unspecified. The notion of forbidden pattern has led to the discovery of several novel tractable classes for the CSP. However, for this field to come of age it is time for a theoretical study of the algebra of patterns. We present a Galois connection between lattices composed of sets of forbidden patterns and sets of generic instances, and investigate its consequences. We then extend patterns to augmented patterns and exhibit a similar Galois connection. Augmented patterns are a more powerful language than flat (i.e. non-augmented) patterns, as we demonstrate by showing that, for any $$k \ge 1$$ k ≥ 1 , instances with tree-width bounded by k cannot be specified by forbidding a finite set of flat patterns but can be specified by a finite set of augmented patterns. A single finite set of augmented patterns can also describe the class of instances such that each instance has a weak near-unanimity polymorphism of arity k (thus covering all tractable language classes).We investigate the power of forbidding augmented patterns and discuss their potential for describing new tractable classes.

scholarly journals Constraint Satisfaction, Logic and Forbidden Patterns

2007 ◽  
Vol 37 (1) ◽  
pp. 132-163 ◽  
Author(s):  
Florent Madelaine ◽  
Iain A. Stewart
Keyword(s):  
Constraint Satisfaction ◽  
Forbidden Patterns

scholarly journals Extending Dual Arc Consistency

2003 ◽  
Vol 17 (05) ◽  
pp. 781-815 ◽  
Author(s):  
S. Nagarajan ◽  
S. D. Goodwin ◽  
A. Sattar
Keyword(s):  
Recent Work ◽  
Structural Transformation ◽  
Constraint Satisfaction ◽  
Dual Representation ◽  
Local Consistency ◽  
Arc Consistency ◽  
Binary Constraint ◽  
Binary Compatibility ◽  
The Given ◽  
Different Levels

Many extensions to existing binary constraint satisfaction algorithms have been proposed that directly deal with nonbinary constraints. Another choice is to perform a structural transformation of the representation of the problem, so that the resulting problem is a binary CSP except that now the original constraints which were nonbinary are replaced by binary compatibility constraints between relations. A lot of recent work has focussed on comparing different levels of local consistency enforceable in the nonbinary representation with the dual representation. In this paper we present extensions to the standard dual encoding that can compactly represent the given CSP using an equivalent dual encoding that contains all the original solutions to the CSP, using constraint coverings. We show how enforcing arc consistency in these constraint covering based encodings, strictly dominates enforcement of generalized arc consistency (GAC) on the primal nonbinary encoding.

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.

Sign in / Sign up

Export Citation Format

Share Document