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

Arangú M., Salido M. A.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 4

733-744

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. Arcconsistency 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.

AND-OR graph with knowledge propagation rules as a model for Constraint Satisfaction Problems

Ligęza A.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

2009

T. 13, z. 2

411-419

In this paper a model for Constraint Satisfaction Problems based on the concept of AND-OR graph is presented. The graph provides a structure to model search-space for alternative solutions. In order to represent auxiliary constraints it is completed with a set of rules for knowledge propagation. The rules can be used for efficient modelling of constraints for knowledge propagation and for detection of inconsistency. An example from the area of automated diagnosis is used to illustrate the application.

W pracy przedstawiono koncepcję zastosowania grafu AND--OR do rozwiązywania problemów z ograniczeniami. Dla efektywnej eliminacji niepoprawnych rozwiązań zastosowano system regułowy. Jest on wykorzystywany do propagacji wiedzy. W przypadku wykrycia niespójności, potencjalne rozwiązanie jest eliminowane. Rozważania przeprowadzono na przykładzie zastosowania proponowanego podejścia do eliminacji niepoprawnych rozwiązań problemu diagnostycznego.