Randomized algorithms
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 threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Approximation algorithms for directed Steiner problems
Journal of Algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
New approaches to covering and packing problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
An approximation algorithm for the group Steiner problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Multi-embedding and path approximation of metric spaces
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Multi-embedding and path approximation of metric spaces
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Asymmetric k-center is log* n-hard to approximate
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Asymmetric k-center is log* n-hard to approximate
Journal of the ACM (JACM)
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
On average throughput and alphabet size in network coding
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
The Set Connector Problem in Graphs
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Multicommodity facility location under group Steiner access cost
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The polymatroid steiner problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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We present an Ω(log2k) lower bound on the integrality ratio of the flow-based relaxation for the Group Steiner Tree problem, where k denotes the number of groups; this holds even for input graphs that are Hierarchically Well-Separated Trees, introduced by Bartal [Symp. Foundations of Computer Science, pp. 184--193, 1996], in which case this lower bound is tight. This relaxation appears to be the only one that have been studied for the problem, as well as for its generalization, the Directed Steiner Tree problem. For the latter problem, our results imply an Ω(log2n/(log logn)2) integrality ratio, where n is the number of vertices in the graph. For both problems, this is the first known lower bound on the integrality ratio that is superlogarithmic in the input size. We also show algorithmically that the integrality ratio for Group Steiner Tree is much better for certain families of instances, which helps pinpoint the types of instances that appear to be most difficult to approximate.