As was described above, the output of MIN-GREEDY's second stage is a minimized set of tag bigrams which is used as a constraint on the first iteration of the third stage, Iterative Model-Fitting.
in order to determine when to stop adding new bigrams during the first two phases, the MIN-GREEDY algorithm must try to find complete tag paths through each sentence in the raw corpus, stopping once a tag path has been found for each one.