The connection between integrality gaps and computational hardness of discrete optimization problems is an intriguing question. In recent years, this connection has prominently figured in severalâ€¦ (More)

We prove that, assuming the Unique Games Conjecture (UGC), every problem in the class of ordering constraint satisfaction problems (OCSP) where each constraint has constant arity is approximationâ€¦ (More)

We establish two results about the inapproximability of the Densest Îº-Subgraph (DÎºS) problem. Both results are of similar flavor: ruling out constant factor approximations in polynomial time for theâ€¦ (More)

2008 49th Annual IEEE Symposium on Foundations ofâ€¦

2008

We prove that approximating the max. acyclic subgraph problem within a factor better than 1/2 is unique games hard. Specifically, for every constant epsiv > 0 the following holds: given a directedâ€¦ (More)

In a beautiful result, Raghavendra established optimal Unique Games Conjecture (UGC)-based inapproximability for a large class of constraint satisfaction problems (CSPs). In the class of CSPs heâ€¦ (More)

2009 24th Annual IEEE Conference on Computationalâ€¦

2009

A permutation constraint satisfaction problem (permCSP) of arity k is specified by a subset Lambda of permutations on $\{1,2,\dots,k\}$. An instance of such a permCSP consists of a set of variablesâ€¦ (More)

These are notes from a mini course on additive combinatorics given in Princeton University on August 23-24, 2007. The lectures were Boaz Barak (Princeton University), Luca Trevisan (University ofâ€¦ (More)