Fast and exact algorithms for some NP-hard 2-clustering problems in the one-dimensional case

Abstract

We consider several well-known optimization 2-clustering (2-partitioning) problems of a finite set of points in Euclidean space. All clustering problems considered are induced by applied problems in Data analysis, Data cleaning, and Data mining. In the general case, all these optimization problems are strongly NP-hard. In the paper, we present a brief overview of the results on the problems computational complexity and on their solvability in the one-dimensional case. We present and propose well-known and new, simple and fast exact algorithms with O(N log N) and O(N) running times for the one-dimensional case of these problems.