Optimal Approximations of the Frequency Moments

We give a one-pass, O~(m^{1-2/k})-space algorithm for estimating the k-th frequency moment of a data stream for any real k>2. Together with known lower bounds, this resolves the main problem left open by Alon, Matias, Szegedy, STOC'96. Our algorithm enables deletions as well as insertions of stream elements.

A Constant-Factor Approximation Algorithm for Embedding Unweighted Graphs into Trees

We present a constant-factor approximation algorithm for computing an embedding of the shortest path metric of an unweighted graph into a tree, that minimizes the multiplicative distortion.

Complex System Classification

The use of terms such as “Engineering Systems”, “System of systems” and others have been coming into greater use over the past decade to denote systems of importance but with implied higher complexity than for the term systems alone. This paper searches for a useful taxonomy or classification scheme for complex Systems. There are two aspects to this problem: 1) distinguishing between Engineering Systems (the term we use) and other Systems, and 2) differentiating among Engineering Systems. Engineering Systems are found to be differentiated from other complex systems by being human-designed and having both significant human complexity as well as significant technical complexity. As far as differentiating among various engineering systems, it is suggested that functional type is the most useful attribute for classification differentiation. Information, energy, value and mass acted upon by various processes are the foundation concepts underlying the technical types.