Computing a minimum vertex cover in graphs and hypergraphs is a well-studied optimizaton problem. While intractable in general, it is well known that on bipartite graphs, vertex c...
Assuming the Unique Games Conjecture (UGC), we show optimal inapproximability results for two classic scheduling problems. We obtain a hardness of 2 − ε for the problem of mini...
Given a k-uniform hypergraph, the Ek-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyperedge. We present a new multilayered PCP constructi...
We show that for k ≥ 3 even the Ω(n) level of the Lasserre hierarchy cannot disprove a random k-CSP instance over any predicate type implied by k-XOR constraints, for example ...
We prove that various geometric covering problems, related to the Travelling Salesman Problem cannot be efficiently approximated to within any constant factor unless P = NP. This ...