Abstract
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 region-restricted 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(nmlog2 n + (nm+nn f )log2 n f ) time, where n f 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 logn + n/ε 2 + n f log2 n f + (nlog2 n f )/(mε 2)) time. We also show how to compute largest clusters and outliers.
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Gudmundsson, J., van Kreveld, M., Narasimhan, G. (2006). Region-Restricted Clustering for Geographic Data Mining. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_37
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DOI: https://doi.org/10.1007/11841036_37
Publisher Name: Springer, Berlin, Heidelberg
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