Both algorithms are aimed at extracting a directed acyclic graph (a hierarchy) between tags from co-occurrence statistics. A detailed description of the algorithms can be found in our paper "Extracting tag hierarchies". They take either the weighted co-occurrence network between the tags as the input, (accompanied by the frequency distribution of the tags), or simply the list of co-occurring tags on the individual objects, (in which case the first step is the preparation of the co-occurrence network). The output is simply the list of directed links between the tags, representing the hierarchy. Both algorithms are implemented in Perl.

Version used in the publication PLoS ONE 8(12): e84133.)
An improved version of algorithm B:
last version and example datasets are here