We study dense instances of several covering problems. An instance of the set cover problem with $m$ sets is dense if there is $\epsilon>0$ such that any element belongs to at least $\epsilon m$ sets. We show that the dense set cover problem can be approximated with the performance ratio ... more >>>

We study small degree graph problems such as Maximum Independent Set and Minimum Node Cover and improve approximation lower bounds for them and for a number of related problems, like Max-B-Set Packing, Min-B-Set Cover, Max-Matching in B-uniform 2-regular hypergraphs. For example, we prove NP-hardness factor of 95/94 for Max-3-Dimensional Matching, ... more >>>

In the set cover problem we are given a collection of $m$ sets whose union covers $[n] = \{1,\ldots,n\}$ and must find a minimum-sized subcollection whose union still covers $[n]$. We investigate the approximability of set cover by an approximation ratio that depends only on $m$ and observe that, for ... more >>>