LRM-Trees: Compressed Indices, Adaptive Sorting, and Compressed Permutations

TL;DR

LRM-Trees provide a versatile framework for data compression, adaptive sorting, and efficient permutation indexing, enabling significant improvements in space and time complexity across various data structure and algorithm applications.

Contribution

This paper introduces new applications of LRM-Trees, including compressed indices for range queries, an adaptive sorting algorithm, and a succinct permutation data structure supporting fast operations.

Findings

Compressed succinct indices for range minimum queries

An adaptive sorting algorithm based on LRM-Trees

A space-efficient permutation data structure supporting direct and indirect application

Abstract

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were 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, from data structures to algorithms: some compressed succinct indices for range minimum queries; a new adaptive sorting algorithm; and a compressed succinct data structure for permutations supporting direct and indirect application in time all the shortest as the permutation is compressible.