Removing redundancy and updating databases

In order to eliminate redundant information in a database one usually uses decomposition or special database design methods to achieve Third Normal Form (or some other normal form like Boyce-Codd Normal Form). This method of database design assumes that the real world satisfies very strong constraints like functional dependencies (fds), without any exceptions. Most databases in "Whatever" Normal Form still contain a large amount of duplicated information, because the real world satisfies very few constraints, but a lot of "almost" constrains. Horizontal Fragments (resulting from Horizontal Decomposition) can be used to separate information with different properties. The different constraints that hold in these fragments can be used to eliminate redundant information in the fragments. We focus on the horizontal decomposition for eliminating exceptions to fds. We show how to update such horizontally decomposed databases in an efficient way. Generating separate horizontal fragments for all desired fds that do not hold in the real world may not be possible (although for every fd there will be a fragment for its exceptions, but the fragments for a number of fds may coincide). The number of fds for which a separate exception fragment can be generated depends on the choice of fds and the order in which they are used. We show that it is possible to find (in polynomial time) the order which leads to the "optimal" decomposition of a relation into horizontal fragments.