Journal of Algorithms
On clustering problems with connected optima in Euclidean spaces
Discrete Mathematics
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Journal of Algorithms
Finding k-cuts within twice the optimal
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Topics in computational geometry
Topics in computational geometry
Approximation algorithms for clustering to minimize the sum of diameters
Nordic Journal of Computing
Approximation Algorithms for Clustering to Minimize the Sum of Diameters
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
On static and dynamic methods for condensation-based privacy-preserving data mining
ACM Transactions on Database Systems (TODS)
Local search study of honeycomb clustering problem for cellular planning
International Journal of Mobile Network Design and Innovation
On the number of separable partitions
Journal of Combinatorial Optimization
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This paper investigates the computational complexity of several clustering problems with special objective functions for point sets in the Euclidean plane. Our strongest negative result is that clustering a set of 3k points in the plane into k triangles with minimum total circumference is NP-hard. On the other hand, we identify several special cases that are solvable in polynomial time due to the special structure of their optimal solutions: The clustering of points on a convex hull into triangles; the clustering into equal-sized subsets of points on a line or on a circle with special objective functions; the clustering with minimal cluster-distances. Furthermore, we investigate clustering of planar point sets into convex quadrilaterals.