Given a complete graph G=(V, E) where each edge is labeled+ or−, the CORRELATION
CLUSTERING problem asks to partition V into clusters to minimize the number of+ edges …

The edge expansion of a subset of vertices S⊆ V in a graph G measures the fraction of
edges that leave S. In a d-regular graph, the edge expansion/conductance Φ (S) of a subset …

We introduce a method for proving lower bounds on the efficacy of semidefinite
programming (SDP) relaxations for combinatorial problems. In particular, we show that the …

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 …

Let Φ be a uniformly random k-SAT formula with n variables and m clauses. We study the
algorithmic task of finding a satisfying assignment of Φ. It is known that satisfying …

We solve a 20-year old problem posed by Yannakakis and prove that there exists no
polynomial-size linear program (LP) whose associated polytope projects to the traveling …

We show that for kges3 even the Omega (n) level of the Lasserre hierarchy cannot disprove
a random k-CSP instance over any predicate type implied by k-XOR constraints, for example …

Given a graph and an integer k, Densest k-Subgraph is the algorithmic task of finding the
subgraph on k vertices with the maximum number of edges. This is a fundamental problem …

We solve a 20-year old problem posed by Yannakakis and prove that no polynomial-size
linear program (LP) exists whose associated polytope projects to the traveling salesman …

We prove super-polynomial lower bounds on the size of linear programming relaxations for
approximation versions of constraint satisfaction problems. We show that for these problems …