MAINTAINING SPATIAL CONSTRAINTS USING A DIMENSION GRAPH APPROACH

Abstract

Efficient algorithms for checking consistency of a set of spatial constraints among spatiotemporal objects are crucial for many practical application systems needing real-time response. This paper is focused on the consistency for directional spatial constraints in a two-dimensional Euclidean space, which is critical in application domains such as geographic information systems, battlefield visualization, transportation, etc. We propose a dimension graph representation to maintain the Euclidean spatial constraints among 2D objects (points, intervals, regions). The basic idea is to project the spatial constraints on both X and Y dimensions, and then to construct a dimension graph on each dimension. The dimension graph representation transforms the problem of consistency checking into the problem of graph cycle detection. Consistency checking for conjunctive constraints can then be achieved in linear time complexity. This approach is much more efficient than competing approaches when there are few disjunctions in the spatial constraints, which are often true in above applications. We also demonstrate that the proposed algorithm can guarantee global consistency.