Beyond Steiner's problem: a VLSI oriented generalization
WG '89 Proceedings of the fifteenth international workshop on Graph-theoretic concepts in computer science
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Spanning Trees---Short or Small
SIAM Journal on Discrete Mathematics
A constant-factor approximation algorithm for the k MST problem (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A 2.5-factor approximation algorithm for the k-MST problem
Information Processing Letters
A polylogarithmic approximation algorithm for the group Steiner tree problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
An approximation algorithm for the covering Steiner problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A 2 + ε approximation algorithm for the k-MST problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
New approaches to covering and packing problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On Network Design Problems: Fixed Cost Flows and the Covering Steiner Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Meet and merge: approximation algorithms for confluent flows
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On network design problems: fixed cost flows and the covering steiner problem
ACM Transactions on Algorithms (TALG)
A Recursive Greedy Algorithm for Walks in Directed Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
Meet and merge: Approximation algorithms for confluent flows
Journal of Computer and System Sciences - Special issue on network algorithms 2005
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
Approximation algorithms for requirement cut on graphs
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
The polymatroid steiner problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Note: The relation of Connected Set Cover and Group Steiner Tree
Theoretical Computer Science
Stochastic vehicle routing with recourse
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Minimum latency submodular cover
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Embedding paths into trees: VM placement to minimize congestion
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Hi-index | 0.02 |
The covering Steiner problem is a generalization of both the k-MST and the group Steiner problems: given an edge-weighted graph, with subsets of vertices called the groups, and a nonnegative integer value (called the requirement) for each group, the problem is to find a minimum-weight tree spanning at least the required number of vertices of every group. When all requirements are equal to 1, this becomes the group Steiner problem, while if there is only one group which contains all vertices of the graph the problem reduces to k-MST with k equal to the requirement of this unique group. We discuss two different (but equivalent) linear relaxations of the problem for the case when the given graph is a tree and construct polylogarithmic approximation algorithms based on randomized LP rounding of these relaxations. By using a probabilistic approximation of general metrics by tree metrics due to Bartal, our algorithms also solve the covering Steiner problem on general graphs with a further polylogarithmic worsening in the approximation ratio.