Recognizing and realizing cactus metrics

Recognizing and realizing cactus metrics

Hayamizu, Momoko (Institute of Statistical Mathematics; Japan Science and Technology Agency)
Huber, Katharina T. (University of East Anglia)
Moulton, Vincent (University of East Anglia)
Murakami, Yukihiro (TU Delft Discrete Mathematics and Optimization)

2020-05-01

The problem of realizing finite metric spaces in terms of weighted graphs has many applications. For example, the mathematical and computational properties of metrics that can be realized by trees have been well-studied and such research has laid the foundation of the reconstruction of phylogenetic trees from evolutionary distances. However, as trees may be too restrictive to accurately represent real-world data or phenomena, it is important to understand the relationship between more general graphs and distances. In this paper, we introduce a new type of metric called a cactus metric, that is, a metric that can be realized by a cactus graph. We show that, just as with tree metrics, a cactus metric has a unique optimal realization. In addition, we describe an algorithm that can recognize whether or not a metric is a cactus metric and, if so, compute its optimal realization in O(n³) time, where n is the number of points in the space.

Algorithms
Cactus metric
Metric realization
Optimal realization
Phylogenetic network

http://resolver.tudelft.nl/uuid:50bd965d-e53e-4f0e-a1e5-dba01e9e620c

https://doi.org/10.1016/j.ipl.2020.105916

0020-0190

Information Processing Letters, 157

Institutional Repository

journal article

© 2020 Momoko Hayamizu, Katharina T. Huber, Vincent Moulton, Yukihiro Murakami