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 the dimension graph is constructed on each dimension. By using the dimension graph representation, the problem of consistency checking is then transformed to a graph cycle detection problem. The consistency checking can be achieved with O(N+E) time as well as space complexity, where N is the number of spatial object, and E is the number of spatial predicates in the constraint. The proposed approach to consistency checking for spatial constraints 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 2 dimensional space. The algorithm can guarantee the global consistency.
Liu, Xuan; Shekhar, Shashi; Chawla, Sanjay.
Consistency Checking for Euclidean Spatial Constraints: A Dimension Graph Approach.
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