Algorithms for clustering data
Algorithms for clustering data
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
Finding k points with minimum diameter and related problems
Journal of Algorithms
On enclosing k points by a circle
Information Processing Letters
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)
Fast spatial clustering with different metrics and in the presence of obstacles
Proceedings of the 9th ACM international symposium on Advances in geographic information systems
Clustering Algorithms
Introduction to Algorithms
Geographic Data Mining and Knowledge Discovery
Geographic Data Mining and Knowledge Discovery
Determining approximate shortest paths on weighted polyhedral surfaces
Journal of the ACM (JACM)
Data Mining: Concepts and Techniques
Data Mining: Concepts and Techniques
Density-based clustering of uncertain data
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
The hunting of the bump: on maximizing statistical discrepancy
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On k-Nearest Neighbor Voronoi Diagrams in the Plane
IEEE Transactions on Computers
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Journal of Computer and System Sciences
A geometric approach to the problem of reconstruction of the sample behavior in hidden dimensions
Pattern Recognition and Image Analysis
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Clustering problems in a complex geographical setting are often required to incorporate the type and extent of land cover within a region. Given a set P of n points in a geographical setting, with the constraint that the points of P can only occur in one type of land cover, an interesting problem is the detection of clusters. First, we extend the definition of clusters and define the concept of a region-restricted cluster that satisfies the following properties: (i) the cluster has sufficient number of points, (ii) the cluster points are confined to a small geographical area, and (iii) the amount of land cover of the specific type in which the points lie is also small. Next, we give efficient exact and approximation algorithms for computing such clusters. The exact algorithm determines all axis-parallel squares with exactly m out of n points inside, size at most some prespecified value, and area of a given land cover type at most another prespecified value, and runs in O(nmlog^2n+(nm+nn"f)log^2n"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+@e too large, and runs in O(nlogn+n/@e^2+n"flog^2n"f+(nlog^2n"f)/(m@e^2)) time. We also show how to compute largest clusters and outliers.