Set Cover 1 Unweighted Set Cover

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...

Approximation Algorithms : Set Cover and Max Cut 1 Unweighted Set

Set Cover Revisited: Hypergraph Cover with Hard Capacities

In this paper, we consider generalizations of classical covering problems to handle hard capacities. In the hard capacitated set cover problem, additionally each set has a covering capacity which we are not allowed to exceed. In other words, after picking a set, we may cover at most a specified number of elements. Based on the classical results by Wolsey, an O(log n) approximation follows for t...

Linear Time Algorithms for Generalized Edge Dominating Set Problems

We prove that a generalization of the edge dominating set problem, in which each edge e needs to be covered be times for all e ∈ E, admits a linear time 2-approximation for general unweighted graphs and that it can be solved optimally for weighted trees. We show how to solve it optimally in linear time for unweighted trees and for weighted trees in which be ∈ {0, 1} for all e ∈ E. Moreover, we ...

Covering Problems with Hard Capacities

We consider the classical vertex cover and set cover problems with the addition of hard capacity constraints. This means that a set (vertex) can only cover a limited number of its elements (adjacent edges) and the number of available copies of each set (vertex) is bounded. This is a natural generalization of the classical problems that also captures resource limitations in practical scenarios. ...