This chapter surveys how semidefinite programming can be used for finding good
approximative solutions to hard combinatorial optimization problems. The chapter begins …

On the Unique Games Conjecture Page 1 On the Unique Games Conjecture Subhash Khot
Courant Institute of Mathematical Sciences, NYU ∗ Abstract This article surveys recently …

Semidefinite programs (SDPs) are a fundamental class of optimization problems with
important recent applications in approximation algorithms, quantum complexity, robust …

The formalism of probabilistic graphical models provides a unifying framework for capturing
complex dependencies among random variables, and building large-scale multivariate …

In semidefinite programming, one minimizes a linear function subject to the constraint that
an affine combination of symmetric matrices is positive semidefinite. Such a constraint is …

Although this may seem a paradox, all exact science is dominated by the idea of
approximation. Bertrand Russell (1872-1970) Most natural optimization problems, including …

We present randomized approximation algorithms for the maximum cut (MAX CUT) and
maximum 2-satisfiability (MAX 2SAT) problems that always deliver solutions of expected …

For many applications a randomized algorithm is either the simplest algorithm available, or
the fastest, or both. This tutorial presents the basic concepts in the design and analysis of …

In this article, we give an overview of efficient algorithms for the approximate and exact
nearest neighbor problem. The goal is to preprocess a dataset of objects (eg, images) so …

We show an optimal data-dependent hashing scheme for the approximate near neighbor
problem. For an n-point dataset in a d-dimensional space our data structure achieves query …