Logic-Based Approach to Incremental Monitoring and Optimization on Strongly Distributed Data Streams.

In this paper, we systematically adopt logical reduction techniques to monitoring and optimization on distributed data streams. The first technique: Feferman-Vaught reductions, which describe how the queries over a disjoint union of data streams can be computed from queries over the components and queries over the index set. The second one: the syntactically defined translation schemes, which describe possible transformations of data. Combination of these two techniques allows us to consider not only monitoring and optimization on disjoin unions of data streams but rather on much richer compositions. We call them strongly distributed data streams. Our approach is applicable to both homogeneous and heterogeneous data streams. While, as a rule, the known approaches provide some approximation of the solution of the original problem, our method derives solutions over the components of a strongly distributed data stream, such that their further proceeding gives a result that is equivalent to the solution of the original problem on the given data stream.