The optimization problem for a subclass of conjunctive queries which i
s formed by the union of the class of fan-out free queries and a subcl
ass of typed fan-out queries is investigated. The typed fan-out querie
s in this class are obtained from simple tableaux by allowing atmost o
ne attribute to violate the simple-tableau property. The optimization
problem for several restricted subsets of typed fan-out queries is alr
eady known to be NP-hard. It is shown that the queries under considera
tion possess several useful properties which are then used to obtain a
n O(n(2)) optimization algorithm based on the implication graph techni
que. The optimization of typed fan-out queries, obtained from simple t
ableaux by allowing atmost two attributes to violate the simple tablea
u property, is shown to be NP-hard. The optimization of simple tableau
x in the presence of functional dependencies is also investigated and
is shown to be NP-hard.