Approximating the dense set-cover problem

Approximating vertex cover in dense hypergraphs

We consider the minimum vertex cover problem in hypergraphs in which every hyperedge has size k (also known as minimum hitting set problem, or minimum set cover with element frequency k). Simple algorithms exist that provide k-approximations, and this is believed to be the best possible approximation achievable in polynomial time. We show how to exploit density and regularity properties of the ...

On Approximating the Corner Cover Problem

The rectilinear polygon cover problem is one in which a certain class of features of a rectilinear polygon of n vertices has to be covered with the minimum number of rectangles included in the polygon. In particular, one can consider covering the entire interior, the boundary and the set of corners of the polygon. These problems have important applications in, for example, storing images and in...

Approximating Min - sum Set Cover 1 Uriel

The Pipelined Set Cover Problem

A classical problem in query optimization is to find the optimal ordering of a set of possibly correlated selections. We provide an abstraction of this problem as a generalization of set cover called pipelined set cover, where the sets are applied sequentially to the elements to be covered and the elements covered at each stage are discarded. We show that several natural heuristics for this NP-...

Approximating the Unweighted k-Set Cover Problem: Greedy Meets Local Search

In the unweighted set-cover problem we are given a set of elements E = {e1, e2, . . . , en} and a collection F of subsets of E. The problem is to compute a sub-collection SOL ⊆F such that ⋃ Sj∈SOL Sj = E and its size |SOL| is minimized. When |S| ≤ k for all S ∈ F we obtain the unweighted k-set cover problem. It is well known that the greedy algorithm is an Hk-approximation algorithm for the unw...