A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Improved methods for approximating node weighted Steiner trees and connected dominating sets
Information and Computation
Steiner tree problem with minimum number of Steiner points and bounded edge-length
Information Processing Letters
Information Processing Letters
Approximations for Steiner trees with minimum number of Steiner points
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
Connected set cover problem and its applications
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Clustering with internal connectedness
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Theoretical Computer Science
Note: The relation of Connected Set Cover and Group Steiner Tree
Theoretical Computer Science
Hi-index | 5.23 |
Given a set V of elements, S a family of subsets of V, and G a connected graph on vertex set S,a connected set cover (CSC) is a subfamily R of S such that every element in V is covered by at least one set of R, and the subgraph G[R] of G induced by R is connected. If furthermore G[R] is k-connected and every element in V is covered by at least m sets in R, then R is a (k,m)-CSC. In this paper, we present two approximation algorithms for the minimum CSC problem, and one approximation algorithm for the minimum (2,m)-CSC problem. Performance ratios are analyzed. These are the first approximation algorithms for CSC problems in general graphs with guaranteed performance ratios.