arXiv subjects

Jérémy Barbay

Publications and source records attributed to Jérémy Barbay.

21 records · Page 2Linked to original sources

arXiv2011

On Compressing Permutations and Adaptive Sorting

Previous compact representations of permutations have focused on adding a small index on top of the plain data $<π(1), π(2),...π(n)>$, in order to efficiently support the application of the inverse or the iterated permutation. In this paper we initiate the study of techniques that exploit the compressibility of the data itself, while retaining efficient computation of $π(i)$ and its inverse. In particular, we focus on exploiting {\em runs}, which are subsets (contiguous or not) of the domain where the permutation is monotonic. Several variants of those types of runs arise in real applications such as inverted indexes and suffix arrays. Furthermore, our improved results on compressed data structures for permutations also yield better adaptive sorting algorithms.

cs.DS↗

arXiv2010

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, 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.

cs.DS↗

arXiv2009

Compressed Representations of Permutations, and Applications

We explore various techniques to compress a permutation $π$ over n integers, taking advantage of ordered subsequences in $π$, while supporting its application $π$(i) and the application of its inverse $π^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $π^k(i)$ of it, of integer functions, and of inverted lists and suffix arrays.

cs.DS↗