I’ll be giving a presentation, open to the public, tomorrow on my research.
Here is my abstract:
The problem of finding maximal empty rectangles in a set of points in 2D and 3D space has been well studied, and efficient algorithms exist to identify maximal rectangles in 2D space. Unfortunately, such efficiency is lacking in higher dimensions where the problem has been shown to be NP complete when the dimensions are included in the input. We compare existing methods and suggest a novel technique to discover interesting maximal empty hyper-rectangles in cases where dimensionality and input size would otherwise make analysis impractical. Applications include big data analysis, recommender systems, automatic knowledge discovery, and query optimization.
Keywords: Maximal Empty Rectangle, Maximal Cuboid, Big Data