### Metrics on Multi-labeled Trees: Interrelationships and Diameter Bounds

Huber, K *(East Anglia)*

Monday 20 June 2011, 15:30-15:50

Seminar Room 1, Newton Institute

#### Abstract

Multi-labeled trees or MUL-trees, for short, are trees whose leaves are labeled by elements of some non-empty finite set $X$ such that more than one leaf may be labeled by the same element of $X$. This class of trees includes phylogenetic trees and tree shapes.
MUL-trees arise naturally in, for example, biogeography and gene evolution studies and also in the area of phylogenetic network reconstruction. In this talk we introduce novel metrics which may be used to compare MUL-trees, most of which generalize
well-known metrics on phylogenetic trees and tree shapes. These metrics can be used, for example, to better understand the space of MUL-trees or to help visualize collections of MUL-trees. In addition, we describe some relationships between the MUL-tree metrics that we present and also give some novel diameter bounds for these metrics.

This is joint work with A. Spillner, University of Greifswald, Germany, and R. Suchecki and V. Moulton, both School of Computing Sciences, University of East Anglia, UK.

#### Presentation

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