Reference: Brinkley, J. F.; Buchanan, B. G.; Altman, R. B.; Duncan, B. S.; & Cornelius, C. W. A Heuristic Refinement Method for Spatial Constraint Satisfaction Problems. January, 1987.
Abstract: The problem of arranging a set of physical objects according to a set of constraints is formulated as a geometric constraint satisfaction problem (GCSP), in which the variables are the objects, the possible locations of the objects are the possible values for the variables, and the constraints are geometric constraints between the objects. A GCSP is type of multi- dimensional constraint satisfaction problem in which the number of objects and/or the number of possible locations per object is too large to permit direct solution by backtrack search. A method is described for reducing these numbers by refinement along two dimensions. The number of objects is reduced by refinement of the structure, representing a group of objects as a single abstract object before considering each object individually. The abstraction used depends on domain specific knowledge. The number of locations per object is reduced by applying node and arc consistency algorithms to refine the accessible volume of each object. Heristics are employed to control the order of operations (and hence to affect the efficiency of search) but not to change the correctness in the sense that no solutions that would be found by backtrack search are eliminated. Application of the method to the problem of protein structure determination is described.
Notes: STAN-CS-87-1142 15 pages.