Polynomial algorithms for nested univariate clustering

doi:10.1016/S0012-365X(01)00135-2

Discrete Mathematics

Volume 245, Issues 1–3, 28 February 2002, Pages 93-105

https://doi.org/10.1016/S0012-365X(01)00135-2 Get rights and content

Under an Elsevier user license

open archive

Abstract

Clique partitioning in Euclidean space $R^{n}$ consists in finding a partition of a given set of $N$ points into $M$ clusters in order to minimize the sum of within-cluster interpoint distances. For $n=1$ clusters need not consist of consecutive points on a line but have a nestedness property. Exploiting this property, an $O (N^{5} M^{2})$ dynamic programming algorithm is proposed. A $θ(N)$ algorithm is also given for the case $M=2$ .

Keywords

Clustering

Clique

Polynomial algorithm

Cited by (0)

^☆: We are grateful to the referees for their careful reading and their many suggestions which led to substantial improvements in the paper's presentation. Research supported by ONR grant N00014-95-1-0917, NSERC (Natural Scientific Research and Engineering Council of Canada) grants GPO105574 and GPO036426, FCAR (Fonds pour la Formation de Chercheurs et l'Aide à la Recherche) grant 95ER1048 and done during visits of the first two authors at University “La Sapienza”, Rome, of the first author at École Polytechnique Fédérale de Lausanne and of the second author at Université de Fribourg.

Discrete Mathematics

Polynomial algorithms for nested univariate clustering☆

Abstract

Keywords