An Arc-Consistency Algorithm for Dynamic and Distributed Constraint Satisfaction Problems

2005 ◽  
Vol 24 (3-4) ◽  
pp. 431-454 ◽  
Author(s):  
Georg Ringwelski
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Distributed Constraint Satisfaction ◽  
Arc Consistency

scholarly journals A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems

2011 ◽  
Vol 21 (4) ◽  
pp. 733-744 ◽  
Author(s):  
Marlene Arangú ◽  
Miguel Salido
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Real Life ◽  
Search Space ◽  
Constraint Satisfaction Problems ◽  
Fine Grained ◽  
Arc Consistency ◽  
Life Problems ◽  
Programming Techniques ◽  
Np Complete

A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems Constraint programming is a powerful software technology for solving numerous real-life problems. Many of these problems can be modeled as Constraint Satisfaction Problems (CSPs) and solved using constraint programming techniques. However, solving a CSP is NP-complete so filtering techniques to reduce the search space are still necessary. Arc-consistency algorithms are widely used to prune the search space. The concept of arc-consistency is bidirectional, i.e., it must be ensured in both directions of the constraint (direct and inverse constraints). Two of the most well-known and frequently used arc-consistency algorithms for filtering CSPs are AC3 and AC4. These algorithms repeatedly carry out revisions and require support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, i.e., they cannot delete any value and consume a lot of checks and time. In this paper, we present AC4-OP, an optimized version of AC4 that manages the binary and non-normalized constraints in only one direction, storing the inverse founded supports for their later evaluation. Thus, it reduces the propagation phase avoiding unnecessary or ineffective checking. The use of AC4-OP reduces the number of constraint checks by 50% while pruning the same search space as AC4. The evaluation section shows the improvement of AC4-OP over AC4, AC6 and AC7 in random and non-normalized instances.

scholarly journals Constraint programming viewed as rule-based programming

2001 ◽  
Vol 1 (6) ◽  
pp. 713-750 ◽  
Author(s):  
KRZYSZTOF R. APT ◽  
ERIC MONFROY
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Constraint Satisfaction Problems ◽  
Rule Based ◽  
Local Consistency ◽  
Arc Consistency ◽  
Computation Process ◽  
Rule Based Approach ◽  
Rule Consistency

We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple first-order formulas. Then we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these explicitly given constraints and limit the computation process to a repeated application of these rules, combined with labeling. We consider two types of rule here. The first type, that we call equality rules, leads to a new notion of local consistency, called rule consistency that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyper-arc consistency in Marriott & Stuckey (1998)). For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rule-based characterization of arc consistency. To show feasibility of this rule-based approach to constraint programming, we show how both types of rules can be automatically generated, as CHR rules of Frühwirth (1995). This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to temporal logic.

FACTORED ARC CONSISTENCY FOR RETE MATCH

1993 ◽  
Vol 02 (02) ◽  
pp. 277-306
Author(s):  
MARK W. PERLIN
Keyword(s):  
Working Memory ◽  
Constraint Satisfaction ◽  
Production Systems ◽  
Constraint Satisfaction Problems ◽  
Unified Framework ◽  
Call Graph ◽  
Quadratic Dependence ◽  
Arc Consistency ◽  
Common Framework ◽  
Graph Factorization

RETE match for production systems and Arc Consistency (AC) filtering are two efficient AI algorithms that are designed for particular constraint satisfaction problems (CSP). Interestingly, it is possible to integrate the two within a common framework, and provide RETE with the lookahead advantages of AC. Unfortunately, the resulting quadratic dependence of AC on working memory (WM) size precludes the application of AC to RETE, since RETE responds to incremental changes in WM. Recent results in AC graph factorization, however, reduce the quadratic dependence to just linear for certain classes of problems, including RETE. In this paper, we present RETE and AC within the unified framework of Call-Graph Caching (CGC) evaluation. We describe factored arc consistency (FAC) and its use in an integrated FAC/RETE algorithm that provides RETE match with AC lookahead. We discuss our implementations, promising initial empirical results, and explore FAC/RETE’s applicability conditions and extensions. We conclude that incorporating factored AC into RETE match is an interesting and potentially useful application of arc consistency methods to the RETE CSP.

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