Trees meet octahedron comparison

Wavelet Trees Meet Suffix Trees

We present an improved wavelet tree construction algorithm and discuss its applications to a number of rank/select problems for integer keys and strings. Given a string of length n over an alphabet of size σ ≤ n, our method builds the wavelet tree in O(n log σ/ √ logn) time, improving upon the state-of-the-art algorithm by a factor of √ log n. As a consequence, given an array of n integers we c...

DART: Dropouts meet Multiple Additive Regression Trees

MART (Friedman, 2001, 2002), an ensemble model of boosted regression trees, is known to deliver high prediction accuracy for diverse tasks, and it is widely used in practice. However, it suffers an issue which we call over-specialization, wherein trees added at later iterations tend to impact the prediction of only a few instances, and make negligible contribution towards the remaining instance...

The Octahedron Abstract Domain

An interesting area in static analysis is the study of numerical properties. Complex properties can be analyzed using abstract interpretation, provided that an adequate abstract domain is defined. Each domain can represent and manipulate a family of properties, providing a different trade-off between the precision and complexity of the analysis. The contribution of this paper is a new numerical...

Octahedron Environment Maps

In this paper, we examine the octahedron as a parameterization scheme to represent environment maps in real-time rendering applications. We discuss two projection schemes and show two convenient unfold mappings to pack the platonic solid into quadratic or rectangular textures. We carry out an analysis and consider rendering performance for interactive applications as well as the quality of repr...

Arrays and the Octahedron Recurrence