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Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary tree-child networks is one of the most studied ones. However, very little is known about the combinatorial structure of these networks. In this paper we address the problem of generating all possible binary tree-child (BTC) networks with a given number of leaves in an efficient way via reduction/augmentation operations that extend and generalize analogous operations for phylogenetic trees, and are biologically relevant. Since our solution is recursive, this also provides us with a recurrence relation giving an upper bound on the number of such networks. We also show how the operations introduced in this paper can be employed to extend the evolutive history of a set of sequences, represented by a BTC network, to include a new sequence. An implementation in python of the algorithms described in this paper, along with some computational experiments, can be downloaded from . [ABSTRACT FROM AUTHOR]

The rapid development of sequencing technology has led to an explosive accumulation of genomic sequence data. Clustering is often the first step to perform in sequence analy- sis, and hierarchical clustering is one of the most commonly used approaches for this purpose. However, it is currently computationally expensive to perform hierarchical clustering of extremely large sequence datasets due to its quadratic time and space complexities. In this paper we developed a new algorithm called ESPRIT-Forest for parallel hierarchical clustering of sequences. The algorithm achieves subquadratic time and space complexity and maintains a high clustering accuracy comparable to the standard method. The basic idea is to organize sequences into a pseudo-metric based partitioning tree for sub-linear time searching of nearest neighbors, and then use a new multiple-pair merging criterion to construct clusters in parallel using multiple threads. The new algorithm was tested on the human microbiome project (HMP) dataset, currently one of the largest published microbial 16S rRNA sequence dataset. Our experiment demonstrated that with the power of parallel computing it is now compu- tationally feasible to perform hierarchical clustering analysis of tens of millions of sequences. The software is available at . [ABSTRACT FROM AUTHOR]