Algorithms for clustering data
Algorithms for clustering data
Finding k points with minimum diameter and related problems
Journal of Algorithms
Static and dynamic algorithms for k-point clustering problems
Journal of Algorithms
Constructing Levels in Arrangements and Higher Order Voronoi Diagrams
SIAM Journal on Computing
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
ACM Computing Surveys (CSUR)
Data mining: concepts and techniques
Data mining: concepts and techniques
Clustering Algorithms
Introduction to Algorithms
An Updated Bibliography of Temporal, Spatial, and Spatio-temporal Data Mining Research
TSDM '00 Proceedings of the First International Workshop on Temporal, Spatial, and Spatio-Temporal Data Mining-Revised Papers
Geographic Data Mining and Knowledge Discovery
Geographic Data Mining and Knowledge Discovery
On k-Nearest Neighbor Voronoi Diagrams in the Plane
IEEE Transactions on Computers
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
An incremental affinity propagation algorithm and its applications for text clustering
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Geodesic disks and clustering in a simple polygon
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Theoretical Computer Science
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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(nmlog2n + (nm+nnf)log2nf) 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 logn + n/ε2 + nflog2nf + (nlog2 nf)/(mε2)) time. We also show how to compute largest clusters and outliers.