2012 IEEE 24th International Conference on Tools with Artificial Intelligence (2000)

Vancouver, British Columbia, Canada

Nov. 13, 2000 to Nov. 15, 2000

ISBN: 0-7695-0909-6

pp: 0333

Xuan Liu , IBM Thomas J. Watson Res. Center, Hawthorne, NY, USA

S. Shekhar , IBM Thomas J. Watson Res. Center, Hawthorne, NY, USA

S. Chawla , IBM Thomas J. Watson Res. Center, Hawthorne, NY, USA

ABSTRACT

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(N/sup 2/) when the number of predicates is much smaller than N/sup 2/ 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.

INDEX TERMS

computational complexity; computational geometry; transforms; consistency checking; Euclidean spatial constraints; dimension graph approach; graph cycle detection; space complexity; spatial objects; spatial predicates; intervals; polygons; two-dimensional space

CITATION

Xuan Liu,
S. Shekhar,
S. Chawla,
"Consistency checking for Euclidean spatial constraints: a dimension graph approach",

*2012 IEEE 24th International Conference on Tools with Artificial Intelligence*, vol. 00, no. , pp. 0333, 2000, doi:10.1109/TAI.2000.889891