Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
SIAM Journal on Computing
Design networks with bounded pairwise distance
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximating the weight of shallow Steiner trees
Discrete Applied Mathematics
Approximation algorithms for directed Steiner problems
Journal of Algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Saving an epsilon: a 2-approximation for the k-MST problem in graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Tighter Bounds for Graph Steiner Tree Approximation
SIAM Journal on Discrete Mathematics
On the Unique Games Conjecture
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The prize-collecting generalized steiner tree problem via a new approach of primal-dual schema
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for the Label-CoverMAX and Red-Blue Set Cover problems
Journal of Discrete Algorithms
Set connectivity problems in undirected graphs and the directed Steiner network problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Tight approximation algorithm for connectivity augmentation problems
Journal of Computer and System Sciences
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Approximating Steiner networks with node weights
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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
Approximating directed buy-at-bulk network design
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
New results on the complexity of the max- and min-rep problems
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Approximating Steiner Networks with Node-Weights
SIAM Journal on Computing
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
Approximating some network design problems with node costs
Theoretical Computer Science
Improved approximation for the directed spanner problem
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Approximating minimum manhattan networks in higher dimensions
ESA'11 Proceedings of the 19th European conference on Algorithms
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We consider the k-Directed Steiner Forest (k-DSF) problem: given a directed graph G = (V, E) with edge costs, a collection D ∈ V x V of ordered node pairs, and an integer k ≤ |D|, find a min-cost subgraph H of G that contains an st-path for (at least) k pairs (s, t) ∈ D. When k = |D|, we get the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems are: Õ(k2/3) for k-DSF by Charikar et al. [2], and O(k1/2+ε) for DSF by Chekuri et al. [3]. For DSF we give an O(nε·min {n4/5,m2/3})-approximation scheme using a novel LP-relaxation seeking to connect pairs via "cheap" paths. This is the first sublinear (in terms of n = |V|) approximation ratio for the problem. For k-DSF we give a simple greedy O(k1/2+ε)-approximation scheme, improving the best known ratio Õ(k2/3) by Charikar et al. [2], and (almost) matching, in terms of k, the best ratio known for the undirected variant [11]. Even when used for the particular case DSF, our algorithm favorably compares to the one of [3], which repeatedly solves linear programs, and uses complex time and space consuming transformations.