The model for data mining on streaming data assumes that there is a buffer of fixed length and a data stream of infinite length and the challenge is to extract patterns, changes, anomalies, and statistically significant structures by examining the data one time and storing records and derived attributes of length less than N. As data grids, data webs, and semantic webs become more common, mining distributed streaming data will become more and more important. The first step when presented with two or more distributed streams is to merge them using a common key. In this paper, we present two algorithms for merging streaming data using a common key. We also present experimental studies showing these algorithms scale in practice to OC-12 networks.

Hrushovski's generalization of the Fraisse construction has provided a rich source of examples in model theory, model theoretic algebra and random graph theory. The construction assigns to a dimension function δ and a class K of finite (finitely generated) models a countable ‘generic’ structure. We investigate here some of the simplest possible cases of this construction. The class K will be a class of finite graphs; the dimension, δ(A), of a finite graph A will be the cardinality of A minus the number of edges of A. Finally and significantly we restrict to classes which are δ-invariant. A class of finite graphs is δ-invariant if membership of a graph in the class is determined (as specified below) by the dimension and cardinality of the graph, and dimension and cardinality of all its subgraphs. Note that a generic graph constructed as in Hrushovski's example of a new strongly minimal set does not arise from a δ-invariant class. We show there are countably many δ-invariant (strong) amalgamation classes of finite graphs which are closed under subgraph and describe the countable generic models for these classes. This analysis provides ω-stable generic graphs with an array of saturation and model completeness properties which belies the similarity of their construction. In particular, we answer a question of Baizhanov (unpublished) and Baldwin [5] and show that this construction can yield an ω-stable generic which is not saturated. Further, we exhibit some ω-stable generic graphs that are not model complete.