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 …

Algorithms in varied fields use the idea of maintaining a distribution over a certain set and
use the multiplicative update rule to iteratively change these weights. Their analyses are …

We give a O (√ log n)-approximation algorithm for the sparsest cut, edge expansion,
balanced separator, and graph conductance problems. This improves the O (log n) …

We develop the algorithmic theory of vertex separators, and its relation to the embeddings of
certain metric spaces. Unlike in the edge case, we show that embeddings into L1 (and even …

Hierarchical graph decompositions play an important role in the design of approximation
and online algorithms for graph problems. This is mainly due to the fact that the results …

From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

In this article, we disprove a conjecture of Goemans and Linial; namely, that every negative
type metric embeds into ℓ1 with constant distortion. We show that for an arbitrarily small …

An n-point metric space (X, D) can be represented by an n× n $ n\times n $ https://s3-euw1-
ap-pe-df-pch-content-public-p. s3. eu-west-1. amazonaws. com/9781315119601/fb8178cb …

We show that the Multicut, Sparsest-Cut, and Min-2CNF≡ Deletion problems are NP-hard to
approximate within every constant factor, assuming the Unique Games Conjecture of Khot …

We give O (√ log n)-approximation algorithms for the MIN UNCUT, MIN 2CNF DELETION,
DIRECTED BALANCED SEPERATOR, and DIRECTED SPARSEST CUT problems. The …