Abstract In this paper, we address the problem of consistencychecking for Euclidean spatial constraints. A dimension graph representation is proposed to maintain the Euclideanspatial 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 prob-lem of consistency checking into the problem of graph cycle detection. Consistency checking can be achieved withO(N+E) time as well as space complexity, where N is the number of spatial objects, and E is the number of spa-tial predicates in the constraint. The proposed approach is faster than O(N 2) when the number of predicates ismuch smaller than N 2 and there are few disjunctions inthe spatial constraint. The dimension graph and consistency checking algorithm can be used for points, intervalsand polygons in two-dimensional space. The algorithm can also guarantee global consistency. Keywords: Euclidean spatial constraint, consistencychecking, dimension graph, directional relationship 1