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Leaf Selection for Maximising Diversity in a Tree

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If you have a question about this talk, please contact David MacKay.

I consider a family of optimisation problems with the following form: given a tree T whose edges have an associated “length”, select (subject to various constraints) a subset S of leaves from T, so that the total length of the (Steiner) subtree that connects them (called “diversity” of S) is maximised. According to the nature of the constraints, the problem has varying computational complexity (reaching NP-hardness) and different algorithmic solutions are devisable, namely a greedy and a pseudo-polynomial dynamic programming algorithm.

I will discuss the relevance of this problem in biology, where some attention has recently been given to the selection of maximally diverse sets of genes, populations or species in the evolutionary tree relating them.

As the leaves don’t need to be biological entities and the tree does not need to reflect evolutionary relationships, I will be particularly curious to hear from the public about any possible applications in their fields of interest.

This talk is part of the Inference Group series.

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