## An algorithm for computing cutpoints in finite metric spaces

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##### Authors

Dress, A.

Huber, K. T.

Koolen, J.

Moulton, V.

Spillner, A.

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##### Abstract

##### Description

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 $O(n^3)$ time.
As a direct consequence, this improves the run time of the aforementioned
$O(n^6)$-algorithm by Hertz and Varone by ``three orders of magnitude''.

Comment: 17 pages, 1 eps-figure

Comment: 17 pages, 1 eps-figure

##### Keywords

Computer Science - Data Structures and Algorithms, Computer Science - Discrete Mathematics