Data fragmentation has been proposed as a solution
for protecting the confidentiality of sensitive
associations when releasing data for publishing or
external storage. To enrich the utility of data
fragments, a recent approach has put forward the idea
of complementing a pair of fragments with some (non
precise, hence loose) information on the association
between them. Starting from the observation that in
presence of multiple fragments the publication of
several independent associations between pairs of
fragments can cause improper leakage of sensitive
information, in this paper we extend loose associations
to operate over an arbitrary number of fragments.
We first illustrate how the publication of multiple loose
associations between different pairs of fragments can
potentially expose sensitive associations, and describe
an approach for defining loose associations among an
arbitrary set of fragments. We investigate how tuples
in fragments can be grouped for producing loose
associations so to increase the utility of queries
executed over fragments. We then provide a heuristics
for performing such a grouping and producing loose
associations satisfying a given level of protection for
sensitive associations, while achieving utility for
queries over different fragments. We also illustrate the
result of an extensive experimental effort over both
synthetic and real datasets, which shows the efficiency
and the enhanced utility provided by our proposal.