Consistency checking for Euclidean spatial constraints: a dimension graph approach

In this paper, we address the problem of consistency checking for Euclidean spatial constraints. A dimension graph representation is proposed to maintain the Euclidean spatial constraints among objects. The basic idea is to project the spatial constraints on both X and Y dimensions, and to construct a dimension graph on each dimension. Using a dimension graph representation transforms the problem of consistency checking into the problem of graph cycle detection. Consistency checking can be achieved with O(N+E) time as well as space complexity, where N is the number of spatial objects, and E is the number of spatial predicates in the constraint. The proposed approach is faster than O(N²) when the number of predicates is much smaller than N² and there are few disjunctions in the spatial constraint. The dimension graph and consistency checking algorithm can be used for points, intervals and polygons in two-dimensional space. The algorithm can also guarantee global consistency