LRM-Trees: Compressed indices, adaptive sorting, and compressed permutations

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks. They have been used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them. We describe how they yield many other convenient results in a variety of areas: compressed indices for range minimum queries on partially sorted arrays, a new adaptive sorting algorithm, and a compressed data structure for permutations supporting direct and inverse application in time inversely proportional to the compressibility of the permutation.