This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

But, perhaps, we should start with a few words about graphs in general. They are, of course,
one of the prime objects of study in Discrete Mathematics. However, graphs are among the …

This is a survey of pseudorandomness, the theory of efficiently generating objects that" look
random" despite being constructed using little or no randomness. This theory has …

We introduce the Bloomier filter, a data structure for compactly encoding a function with
static support in order to support approximate evaluation queries. Our construction …

We give an improved explicit construction of highly unbalanced bipartite expander graphs
with expansion arbitrarily close to the degree (which is polylogarithmic in the number of …

Although there are many advanced and specialized texts and handbooks on algorithms,
until now there was no book that focused exclusively on the wide variety of data structures …

A locally decodable code encodes n-bit strings x in m-bit codewords C (x), in such a way that
one can recover any bit xi from a corrupted codeword by querying only a few bits of that …

The main concrete result of this paper is the first explicit construction of constant degree
lossless expanders. In these graphs, the expansion factor is almost as large as possible:(1 …

This book is a graduate-level textbook on data structures. A data structure is a method1 to
realize a set of operations on some data. The classical example is to keep track of a set of …

A Bloom filter is a very compact data structure that supports approximate membership
queries on a set, allowing false positives. We propose several new variants of Bloom filters …