Discrete optimization problems are everywhere, from traditional operations research
planning (scheduling, facility location and network design); to computer science databases; …

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 Programming (SDP) is one of the strongest algorithmic techniques used in the
design of approximation algorithms. In recent years, Unique Games Conjecture (UGC) has …

Subexponential time approximation algorithms are presented for the Unique Games and
Small-Set Expansion problems. Specifically, for some absolute constant c, the following two …

Over the last twenty years, an exciting interplay has emerged between proof systems and
algorithms. Some natural families of algorithms can be viewed as a generic translation from …

We study the APPROXCOLORING q (Q) problem: Given a graph G, decide whether χ (G)≤
q or χ (G)≥ Q. We derive conditional hardness for this problem for any constant 3≤ q< Q …

Segmentation is an important step in medical imaging to acquire qualitative measurements
such as the location of the desired objects and also for quantitative measurements such as …

In a two player game, a referee asks two cooperating players (who are not allowed to
communicate) questions sampled from some distribution and decides whether they win or …

We consider the k-balanced partitioning problem, where the goal is to partition the vertices
of an input graph G into k equally sized components, while minimizing the total weight of the …

We present an efficient algorithm to find a good solution to the Unique Games problem when
the constraint graph is an expander. We introduce a new analysis of the standard SDP in …