Approximation algorithms for NP-hard problems
STOC '97 Proceedings of the twenty-ninth 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
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
New approximation techniques for some ordering problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
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
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
Approximating the Domatic Number
SIAM Journal on Computing
Integrality ratio for group Steiner trees and directed steiner trees
SODA '03 Proceedings of the fourteenth 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
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On metric ramsey-type phenomena
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
New hardness results for congestion minimization and machine scheduling
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the approximability of some network design problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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 near-tight approximation lower bound and algorithm for the kidnapped robot problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Planning Tours of Robotic Arms among Partitioned Goals
International Journal of Robotics Research
On the complexity of approximating tsp with neighborhoods and related problems
Computational Complexity
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
Bounded-hops power assignment in ad hoc wireless networks
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
The NP-completeness column: The many limits on approximation
ACM Transactions on Algorithms (TALG)
On the partial terminal Steiner tree problem
The Journal of Supercomputing
Set connectivity problems in undirected graphs and the directed Steiner network problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On the approximability of some network design problems
ACM Transactions on Algorithms (TALG)
Efficiently enumerating results of keyword search over data graphs
Information Systems
Tight approximation algorithm for connectivity augmentation problems
Journal of Computer and System Sciences
The Set Connector Problem in Graphs
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Inapproximability of Survivable Networks
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Approximation algorithms for group prize-collecting and location-routing problems
Discrete Applied Mathematics
Improved approximating algorithms for Directed Steiner Forest
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Inapproximability of survivable networks
Theoretical Computer Science
Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Approximating Node-Connectivity Augmentation Problems
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
Bounded-hops power assignment in ad hoc wireless networks
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Mobile real-time group communication service
INFOCOM'10 Proceedings of the 29th conference on Information communications
A polylogarithmic approximation for computing non-metric terminal Steiner trees
Information Processing Letters
A QPTAS for TSP with fat weakly disjoint neighborhoods in doubling metrics
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Tree embeddings for two-edge-connected network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximation algorithms for optimal decision trees and adaptive TSP problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Approximation algorithms for the directed k-tour and k-stroll problems
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Set connectivity problems in undirected graphs and the directed steiner network problem
ACM Transactions on Algorithms (TALG)
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
Nearest keyword search in XML documents
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Improved approximation algorithms for Directed Steiner Forest
Journal of Computer and System Sciences
Approximating rooted Steiner networks
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The generalized deadlock resolution problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Approximating fault-tolerant group-Steiner problems
Theoretical Computer Science
Multicommodity facility location under group Steiner access cost
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On LP-based approximability for strict CSPs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Tight approximation algorithm for connectivity augmentation problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
The polymatroid steiner problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
On approximating the TSP with intersecting neighborhoods
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
The 1-neighbour knapsack problem
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Note: The relation of Connected Set Cover and Group Steiner Tree
Theoretical Computer Science
An approximation algorithm for directed shallow Steiner trees
Proceedings of the 3rd International Conference on Information and Communication Systems
Minimum latency submodular cover
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
The knapsack problem with neighbour constraints
Journal of Discrete Algorithms
Multi-rooted greedy approximation of directed steiner trees with applications
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
On some network design problems with degree constraints
Journal of Computer and System Sciences
On the approximability of Dense Steiner Problems
Journal of Discrete Algorithms
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We provide the first hardness result of a polylogarithmic approximation ratio for a natural NP-hard optimization problem. We show that for every fixed ε0, the GROUP-STEINER-TREE problem admits no efficient log2-ε k approximation, where k denotes the number of groups (or, alternatively, the input size), unless NP has quasi polynomial Las-Vegas algorithms. This hardness result holds even for input graphs which are Hierarchically Well-Separated Trees, introduced by Bartal [FOCS, 1996]. For these trees (and also for general trees), our bound is nearly tight with the log-squared approximation currently known. Our results imply that for every fixed ε0, the DIRECTED-STEINER TREE problem admits no log2-ε n--approximation, where n is the number of vertices in the graph, under the same complexity assumption.