Good morning,
An algorithm like PrefixSpan uses an horizontal database and do database projections. PrefixSpan is said to use a "pattern growth" approach.
For me, I categorize the algorithms as follows:
PrefixSpan: Horizontal database, pattern-growth, database projection, do a depth-first search
CM-SPADE and
SPAM: Vertical database encoded as bitvectors, generate candidates, do a depth-first search
GSP: Vertical database, generate candidates, do a breadth first search
FreeSpan: patterngrowth, horizontal database I think... and probably also do database projection but I dont remember
and there are other algorithms.
...
If you did not read my
survey of sequential pattern mining, it gives some good overview.
Best regards,