Szemerédi's Regularity Lemma is an important tool in discrete mathematics. It says that, in
some sense, all graphs can be approximated by random-looking graphs. Therefore the …

Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical
computer science will welcome the new edition of this book.”-MAA Reviews Maintaining a …

Historically, there is a close connection between geometry and optImization. This is
illustrated by methods like the gradient method and the simplex method, which are …

Additive combinatorics is the theory of counting additive structures in sets. This theory has
seen exciting developments and dramatic changes in direction in recent years thanks to its …

In this paper, we consider the question of determining whether a function f has property P or
is ε-far from any function with property P. A property testing algorithm is given a sample of …

We consider the problem of approximating a given m× n matrix A by another matrix of
specified rank k, which is smaller than m and n. The Singular Value Decomposition (SVD) …

Biological and engineered networks have recently been shown to display network motifs: a
small set of characteristic patterns that occur much more frequently than in randomized …

Szemer\''edi''s Regularity Lemma is an important tool in discrete mathematics. It says that, in
some sense, all graphs can be approximated by random-looking graphs. Therefore the …

m× n matrix A with entries between say− 1 and 1, and an error parameter ε between 0 and 1,
we find a matrix D (implicitly) which is the sum of simple rank 1 matrices so that the sum of …

Random graphs have proven to be one of the most important and fruitful concepts in modern
Combinatorics and Theoretical Computer Science. Besides being a fascinating study …