An Improved Approximation Ratio for the Covering Steiner Problem

A note on the Covering Steiner Problem

A randomized approximation algorithm for the undirected and directed covering Steiner Problems is presented. The algorithm is based on a randomized reduction to a problem called 12 -Group Steiner. For the undirected case, the approximation ratio matches the approximation ratio of Konjevod et al. [KRS01]. However, our approach is a lot simpler. For the directed covering Steiner this gives an O(n...

On the Covering Steiner Problem

The Covering Steiner problem is a common generalization of the k-MST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edge-costs, and some subsets of vertices called groups, with each group being equipped with a non-negative integer value (called its requirement); the problem is to find a minimum-cost tree which spans at least the requ...

Elementary Approximation Algorithms for Prize Collecting Steiner Tree Problems

This paper deals with approximation algorithms for the prize collecting generalized Steiner forest problem, defined as follows. The input is an undirected graph G= (V ,E), a collection T = {T1, . . . , Tk}, each a subset of V of size at least 2, a weight function w :E → R+, and a penalty function p :T → R+. The goal is to find a forest F that minimizes the cost of the edges of F plus the penalt...

An Approximation Algorithm for the Covering Steiner Problem

Approximating dense cases of covering problems

We study dense instances of several covering problems An in stance of the set cover problem with m sets is dense if there is such that any element of the ground set X belongs to at least m sets We show that the dense set cover problem can be approximated with the performance ratio c log jX j for any c though it is unlikely to be NP hard A polynomial time approximation scheme is constructed for ...