Gonzalo Navarro,

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


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

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

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