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Metrics on Multi-labeled Trees: Interrelationships and Diameter Bounds

Monday 20th June 2011 - 15:30 to 15:50
INI Seminar Room 1
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.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons