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...
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...
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...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...
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 ...