Editing Apriori algorithm (section)

== Limitations ==

Apriori, while historically significant, suffers from a number of inefficiencies or trade-offs, which have spawned other algorithms.  Candidate generation generates large numbers of subsets (The algorithm attempts to load up the candidate set, with as many as possible subsets before each scan of the database).  Bottom-up subset exploration (essentially a breadth-first traversal of the subset lattice)  finds any maximal subset S only after all <math>2^{|S|}-1</math> of its proper subsets.

The algorithm scans the database too many times,  which reduces the overall performance. Due to this, the algorithm assumes that the database is permanently in the memory. 

Also, both the time and space complexity of this algorithm are very high: <math>O\left(2^{|D|}\right)</math>, thus exponential, where <math>|D|</math> is the horizontal width (the total number of items) present in the database.

Later algorithms such as [[Max-Miner]]<ref>{{cite journal|author=Bayardo Jr, Roberto J.|title=Efficiently mining long patterns from databases|journal=ACM SIGMOD Record |volume=27|issue=2|year=1998|pages=85–93 |doi=10.1145/276305.276313 |url=http://www.cs.sfu.ca/CourseCentral/741/jpei/readings/baya98.pdf}}</ref> try to identify the maximal frequent item sets without enumerating their subsets, and perform "jumps" in the search space rather than a purely bottom-up approach.