The Metric Cutpoint Partition Problem

Let G = (V, E, w) be a graph with vertex and edge sets V and E, respectively, and w : E IR+ a function which assigns a positive weight or length to each edge of G. G is called a realization of a finite metric space (M, d), with M = {1, ..., n} if and only if {1, ..., n} V and d(i, j) is equal to the length of the shortest chain linking i and j in G i, j = 1, ..., n. A realization G of (M, d), is said optimal if the sum of its weights is minimal among all the realizations of (M, d). A cutpoint in a graph G is a vertex whose removal strictly increases the number of connected components of G. The Metric Cutpoint Partition Problem is to determine if a finite metric space (M, d) has an optimal realization containing a cutpoint. We prove in this paper that this problem is polynomially solvable. We also describe Supported by grant PA002-104974/2 from the Swiss National Science Foundation. Published in Journal of classification, 2008, vol. 25, no. 2, p. 159-175 which should be cited to refe...

• Type: Journal
• Year: 2008
• Where: CLASSIFICATION
• Authors: Alain Hertz, Sacha Varone
• Keywords: CLASSIFICATION 2008, Edge Sets, Finite Metric Space, Positive Weight