Fast and fully-automated histograms for large-scale data sets

G-Enum histograms are a new fast and fully automated method for irregular histogram construction. By framing construction as density estimation problem its automation model selection task, these leverage the Minimum Description Length principle (MDL) to derive two different criteria. Several proven theoretical results about criteria give insights their asymptotic behavior used speed up optimisation. These insights, combined greedy search heuristic, construct in linearithmic time rather than polynomial incurred by previous works. The capabilities of proposed MDL illustrated with reference other methods literature, both on synthetic large real-world data sets.