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Typing methods are widely used in the surveillance of infectious diseases, outbreaks investigation and studies of the natural history of an infection. Moreover, their use is becoming standard, in particular with the introduction of high-throughput sequencing. On the other hand, the data being generated are massive and many algorithms have been proposed for a phylogenetic analysis of typing data, addressing both correctness and scalability issues. Most of the distance-based algorithms for inferring phylogenetic trees follow the closest pair joining scheme. This is one of the approaches used in hierarchical clustering. Moreover, although phylogenetic inference algorithms may seem rather different, the main difference among them resides on how one defines cluster proximity and on which optimization criterion is used. Both cluster proximity and optimization criteria rely often on a model of evolution. In this work, we review, and we provide a unified view of these algorithms. This is an important step not only to better understand such algorithms but also to identify possible computational bottlenecks and improvements, important to deal with large data sets.