On the Complexity of Clustering with Relaxed Size Constraints [chapter]

Massimiliano Goldwurm, Jianyi Lin, Francesco Saccà
2016 Lecture Notes in Computer Science  
We study the computational complexity of the problem of computing an optimal clustering {A1, A2, ..., A k } of a set of points assuming that every cluster size |Ai| belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the 1-norm an analogous procedure known for the 2-norm. Moreover, we prove that in the Euclidean
more » ... ane, i.e. assuming dimension 2 and 2-norm, the problem is NP-hard even with size constraints set reduced to M = {2, 3}.
doi:10.1007/978-3-319-41168-2_3 fatcat:g4uouolskzaqtds2ccl4tefwiy