Consistency checking for Euclidean spatial constraints: A dimension graph approach

Abstract

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.