▁having ▁no ▁tim est amps ▁( D NA ▁sequ encing ). ▁Each ▁transaction ▁is ▁seen ▁as ▁a ▁set ▁of ▁items ▁( an ▁item set ). ▁Given ▁a ▁threshold ▁, ▁the ▁Ap ri ori ▁algorithm ▁ident ifies ▁the ▁item ▁sets ▁which ▁are ▁subsets ▁of ▁at ▁least ▁ ▁transactions ▁in ▁the ▁database . ▁ ▁Ap ri ori ▁uses ▁a ▁" bottom ▁up " ▁approach , ▁where ▁frequent ▁subsets ▁are ▁extended ▁one ▁item ▁at ▁a ▁time ▁( a ▁step ▁known ▁as ▁candidate ▁generation ), ▁and ▁groups ▁of ▁candidates ▁are ▁tested ▁against ▁the ▁data . ▁ ▁The ▁algorithm ▁termin ates ▁when ▁no ▁further ▁successful ▁extensions ▁are ▁found . ▁ ▁Ap ri ori ▁uses ▁bread th - first ▁search ▁and ▁a ▁Hash ▁tree ▁structure ▁to ▁count ▁candidate ▁item ▁sets ▁efficiently . ▁It ▁generates ▁candidate ▁item ▁sets ▁of ▁length ▁ ▁from ▁item ▁sets ▁of ▁length ▁. ▁ ▁Then ▁it ▁pr unes ▁the ▁candidates ▁which ▁have ▁an ▁inf re quent ▁sub ▁pattern . ▁ ▁According ▁to ▁the ▁down ward ▁closure ▁lemma , ▁the ▁candidate ▁set ▁contains ▁all ▁frequent ▁- length ▁item ▁sets . ▁After ▁that , ▁it ▁sc ans ▁the ▁transaction ▁database ▁to ▁determine ▁frequent ▁item ▁sets ▁among ▁the ▁candidates . ▁ ▁The ▁pseudo ▁code ▁for ▁the ▁algorithm ▁is ▁given ▁below ▁for ▁a ▁transaction ▁database ▁, ▁and ▁a ▁support ▁threshold ▁of ▁. ▁Us ual ▁set ▁the or etic ▁notation ▁is ▁employed , ▁though ▁note ▁that ▁ ▁is ▁a ▁mult is et . ▁ ▁is ▁the ▁candidate ▁set ▁for ▁level ▁. ▁At ▁each ▁step , ▁the ▁algorithm ▁is ▁assumed ▁to ▁generate