# Dynamic Entropy-Compressed Sequences and Applications

**Gonzalo Navarro**,

**Departamento de Ciencias de Computación (DCC), Universidad de Chile** –

## Abstract:

Data structures are called succinct when they take little space (meaning

usually of lower order) compared to the data they give access to. A more

ambitious challenge is that of compressed data structures, which aim at

operating within space proportional to that of the compressed data they give

access to. Designing compressed data structures goes beyond compression in the

sense that the data must be manageable in compressed form without first

decompressing it. This is a trend that has gained much attention in recent

years.

In this talk we will introduce a simple data structure for managing bit

sequences, so that the space required is essentially that of the zero-order

entropy of the sequence, and the operations of inserting/deleting bits,

accessing a bit position, and computing rank/select over the sequence, can all

be done in logarithmic time. Rank operation gives the number of 1 (or 0) bits

up to a given position, whereas select gives the position of the j-th 1 (or 0)

bit in the sequence.

This basic result has a surprising number of consequences. We show how it

permits obtaining novel solutions to the dynamic partial sums with indels

problem, dynamic wavelet trees, and dynamic compressed full-text indexes.

Date: 2006-Oct-09 Time: 16:00:00 Room: 336

For more information:

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### Workshop “Metabolism and mathematical models: Two for a tango” – 2nd Edition

**Title: ** Workshop Metabolism and mathematical models: Two for a tango – 2nd Edition

**Dates:** October 25-26, 2022

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The topic of this workshop is metabolism in general, with a special focus, although not exclusive, on parasitology. Besides an exploration of the biological, biochemical and biomedical aspects, the workshop will also aim at presenting some of the mathematical modelling, algorithmic theory and software development that have become crucial to explore such aspects.

This workshop is being organised in the context of two projects, both with the Inria European Team Erable. One of the projects involves a partnership with the University of São Paulo (USP), in São Paulo, Brazil, more specifically the Institute of Mathematics and Statistics (IME) and the Institute of Biomedical Sciences – Inria Associated Team Capoeira – and the other involves the Inesc-ID/IST in Portugal, ETH in Zürich and EMBL in Heidelberg – H2020 Twinning Project Olissipo.

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