Formalizing local propagation in constraint maintenance systems
Local propagation is one of the most simple and general ways to maintain the consistency of constraint problems. When some variable's values are changed or when new constraints are added, it allows to incrementally resatisfy a set of constraints by calling local solving methods. This is particularly useful for interactive applications in computer graphics including geometric design and user interface construction.
However, the great weakness of local propagation comes from cycles in the constraint graph so that local propagation is generally viewed as a weak paradigm that should be assisted by more powerful solvers. We claim that local propagation is powerful enough to tackle complex constraint maintenance problems, provided that the solving methods are expressed in a sufficiently general formalism which allows the user to express any solving method in a natural way. Thus, local propagation should be considered the main constraint maintenance engine that can pilot numeric solvers within this general formalism. This paper presents this formalism and a local propagation algorithm in two steps that can handle it.
KeywordsLocal Propagation Method Formalism Acyclic Directed Graph Global Method Constraint Problem
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- 1.P. Berlandier. A Study of Constraint Interpretation Mechanisms and of their Integration in a Knowledge Representation Language. PhD thesis, University of Nice, 1992. (in french).Google Scholar
- 2.A. Borning. ThingLab: A Constraint-Oriented Simulation Laboratory. PhD thesis, Stanford University, 1979.Google Scholar
- 4.B. Chabrier. Interfaces par contraintes graphiques. PhD thesis, Université de Nice Sophia-Antipolis, 1993.Google Scholar
- 5.B. Freeman-Benson, J. Maloney, and A. Borning. An incremental constraint solver. Communications of the ACM, 33(1), 1990.Google Scholar
- 6.J. Gosling. Algebraic Constraints. PhD thesis, Carnegie-Mellon University, 1983.Google Scholar
- 7.J. Maloney. Using Constraints for User Interface Construction. PhD thesis, University of Washington, August 1991. PhD Thesis, published as Departement of Computer Science and Engineering Technical Report 91-08-12.Google Scholar
- 8.M. Sannella. The skyblue constraint solver and its applications. In Proc. workshop PPCP, Rhode Island, USA, 1993.Google Scholar
- 9.M. Sannella. The skyblue constraint solver. Technical Report 92-07-02, Department of Computer Science and Engineering, University of Washington, February 1993.Google Scholar
- 10.M. Sannella and A. Borning. Multi-garnet: Integrating multi-way constraints with garnet. Technical Report 92-07-01, Department of Computer Science and Engineering, University of Washington, September 1992.Google Scholar
- 11.G. Steele. The Definition and Implementation of a Computer Programming Language Based on Constraints. PhD thesis, Massachusetts Institute of Technology, 1980.Google Scholar