ε-approximations of k-label spaces

Relative ε-Approximations in Geometry∗

We re-examine relative ε-approximations, previously studied in [Pol86, Hau92, LLS01, CKMS06], and their relation to certain geometric problems. We give a simple constructive proof of their existence in general range spaces with finite VC-dimension, and of a sharp bound on their size, close to the best known one. We then give a construction of smaller-size relative ε-approximations for range spa...

The Communication Complexity of Distributed ε-Approximations

Data summarization is an effective approach to dealing with the “big data” problem. Whiledata summarization problems traditionally have been studied is the streaming model, the focus isstarting to shift to distributed models, as distributed/parallel computation seems to be the only viableway to handle today’s massive data sets. In this paper, we study ε-approximations, a classic...

ε-weakly Chebyshev subspaces and quotient spaces

Algorithms for ε-approximations of Terrains

Consider a point set D with a measure function μ : D → R. Let A be the set of subsets of D induced by containment in a shape from some geometric family (e.g. axis-parallel rectangles, half planes, balls, k-oriented polygons). We say a range space (D,A) has an ε-approximation P if

2DV Nonlinear k-ε Turbulence Modeling of Stratified Flows

The commonly used linear k-ε turbulence model is shown to be incapable of accurate prediction of turbulent flows, where non-isotropy is dominant. Two examples of non-isotropic flows, which have a wide range of applications in marine waters, are saline water flow and the stratified flows due to temperature gradients. These relate to stratification and consequently, variation of density through...