TY - JOUR
T1 - An algorithm for computing cutpoints in finite metric spaces
AU - Dress, Andreas W. M.
AU - Huber, Katharina T.
AU - Koolen, Jacobus
AU - Moulton, Vincent
AU - Spillner, Andreas
PY - 2010
Y1 - 2010
N2 - The theory of the tight span, a cell complex that can be associated to every metric D, offers a unifying view on existing approaches for analyzing distance data, in particular for decomposing a metric D into a sum of simpler metrics as well as for representing it by certain specific edge-weighted graphs, often referred to as realizations of D. Many of these approaches involve the explicit or implicit computation of the so-called cutpoints of (the tight span of) D, such as the algorithm for computing the “building blocks” of optimal realizations of D recently presented by A. Hertz and S. Varone. The main result of this paper is an algorithm for computing the set of these cutpoints for a metric D on a finite set with n elements in O(n3) time. As a direct consequence, this improves the run time of the aforementioned O(n6)-algorithm by Hertz and Varone by “three orders of magnitude”.
AB - The theory of the tight span, a cell complex that can be associated to every metric D, offers a unifying view on existing approaches for analyzing distance data, in particular for decomposing a metric D into a sum of simpler metrics as well as for representing it by certain specific edge-weighted graphs, often referred to as realizations of D. Many of these approaches involve the explicit or implicit computation of the so-called cutpoints of (the tight span of) D, such as the algorithm for computing the “building blocks” of optimal realizations of D recently presented by A. Hertz and S. Varone. The main result of this paper is an algorithm for computing the set of these cutpoints for a metric D on a finite set with n elements in O(n3) time. As a direct consequence, this improves the run time of the aforementioned O(n6)-algorithm by Hertz and Varone by “three orders of magnitude”.
U2 - 10.1007/s00357-010-9055-7
DO - 10.1007/s00357-010-9055-7
M3 - Article
VL - 27
SP - 158
EP - 172
JO - Journal of Classification
JF - Journal of Classification
IS - 2
ER -