Region-Restricted Clustering for Geographic Data Mining

Cluster detection for a set P of n points in geographic situations is usually dependent on land cover or another thematic map layer. This occurs for instance if the points of P can only occur in one land cover type. We extend the definition of clusters to regionrestricted clusters, and give efficient algorithms for exact computation and approximation. The algorithm determines all axis-parallel squares with exactly m out of n points inside, size at most some prespepcified value, and area of a given land cover type at most another prespecified value. The exact algorithm runs in O(nm log n + (nm + nnf ) log 2 nf ) time, where nf is the number of edges that bound the regions with the given land cover type. The approximation algorithm allows the square to be a factor 1 + ε too large, and runs in O(n log n+n/ε +nf log 2 nf +(n log 2 nf )/(mε )) time. We also show how to compute largest clusters and outliers.