Hereditarily optimal realizations of consistent metrics

Dress, Andreas, Huber, Katharina T., Lesser, Alice and Moulton, Vincent ORCID: (2006) Hereditarily optimal realizations of consistent metrics. Annals of Combinatorics, 10 (1). pp. 63-67. ISSN 0218-0006

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One of the main problems in phylogenetics is to find good approximations of metrics by weighted trees. As an aid to solving this problem, it could be tempting to consider optimal realizations of metrics—the guiding principle being that, the (necessarily unique) optimal realization of a tree metric is the weighted tree that realizes this metric. And, although optimal realizations of arbitrary metrics are, in general, not trees, but rather weighted networks, one could still hope to obtain a phylogenetically informative representation of a given metric, maybe even more informative than the best approximating tree. However, optimal realizations are not only difficult to compute, they may also be non-unique. Here we focus on one possible way out of this dilemma: hereditarily optimal realizations. These are essentially unique, and can be described in a rather explicit way. In this paper, we recall what a hereditarily optimal realization of a metric is and how it is related to the 1-skeleton of the tight span of that metric, and we investigate under what conditions it coincides with this 1-skeleton. As a consequence, we will show that hereditarily optimal realizations for consistent metrics, a large class of phylogentically relevant metrics, can be computed in a straight-forward fashion.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Depositing User: Vishal Gautam
Date Deposited: 21 May 2011 11:53
Last Modified: 24 Oct 2022 01:47
DOI: 10.1007/s00026-006-0274-x

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