Semantic Decomposition for Solving Distance Constraints
نویسندگان
چکیده
Numerical constraint problems occurs in numerous applications. Consistency techniques on finite domains have been adapted to handle continuous CSP(e.g. 2B-consistency, kBconsistency1, Box-consistency2, . . .). Roughly speaking, these local filtering methods compute an external approximation of the solution space. That is to say, intervals the bounds of which are local consistents. Thus, this external approximation still contains a huge number of local inconsistent values. Splitting techniques are often used to isolate individual solutions.However, these techniques are ineffectivewhen the domain contains continuous subspaces of solutions. Moreover, they do not take advantage of the semantic of the constraints for splitting the intervals. We introduce here a pruning technique, calledLDF(LocalDecompositionFiltering)3, for solving systems of distance equations. Thismethod is based on a local decomposition of the domains which is guided by the properties of the distance constraints(convexity andmonotonicity).More precisely, the domains of the coordinates of two points involved in a constraint c is decomposed using the properties of c(see figure 1). The canonical form of the distance equations(X2 + Y 2 − D2 = 0) identifies the monotonous and convex parts on R+ × R+, R+ × R−, R− × R+ and R− × R−.
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