Possible Extensions and Open Problems - Repairing and Querying Databases under Aggregate Constraints - page 53

such as functional dependencies and inclusion dependencies. The results stated here
are not straightforwardly applicable to this case, since they are strongly based on
the assumption that no repair can delete or insert tuples.

6.2 Dealing with Different Forms of Queries

It is easy to see that all the complexity results reported in Table 3.1 for CQA and
STEADY - CQA still hold for quantifier-free conjunctive queries, i.e., queries of the
form Q

)= i = 1 R i ( ( x x i ) . In this case, CQA becomes the problem of deciding, for a

fixed a, whether Q is true in every repair. This obviously boils down to applying

n CQA instances for atomic queries (one for each R i ). Another straightforward ex-
tension is that of allowing multiple relations to be specified in the

( a )

clause of
aggregate queries: this does not affect the results stated in Chapter 5, and in particu-
lar the correctness of our strategy for computing the range-consistent query answer.
However, other extensions deserve deeper investigation. In particular, from a the-
oretical standpoint, it will be interesting to remove the assumption that measure
attributes are bounded in value which has been exploited in the computation of
range-consistent answers. In fact, this removal implies that the boundaries of the
range-consistent answers can be

FROM

: this makes it necessary to revise the strategy
for computing consistent answers and make it able to detect this case.

± ∞

6.3 Dealing with Different Minimality Semantics

It is worth noting that the framework presented in this topic can be easily refined to
work in those cases where it is more appropriate to decide the reasonableness of a
repair on the basis of the set (resp., the number) of digits changed, instead of the set
(resp., the number) of numerical values changed. In fact, intuitively enough, all the
arguments and strategies used to assess the complexity characterization provided
in this work can be easily adapted in the presence of the new semantics working
at digit-level, when a bound on the number of digits of each measure attribute is
known. Basically, in order to deal with this new semantics starting from the results
stated in this topic, it suffices to observe that any numerical value with K digits can
be viewed as the weighted sum of K distinct numerical values. Observe that the as-
sumption that the maximum number of digits is known for the values of measure
attributes is natural in many application contexts (for instance, in our running ex-
ample, the measure values occurring in the Balance Sheets published by small or
medium enterprises are unlikely to consist of more than 8 digits).
In some application contexts, it may be convenient to decide the reasonableness
of a repair by considering the differences between the values in the original and
the repaired databases. This aspect was considered in [12], where LS-minimal re-
pairs were introduced, i.e., repairs having minimum LS-distance from the original