The steiner problem with edge lengths 1 and 2,
Information Processing Letters
When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
SIAM Journal on Computing
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
On the bidirected cut relaxation for the metric Steiner tree problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A new approximation algorithm for the Steiner tree problem with performance ratio 5/3
Journal of Algorithms
Provisioning a virtual private network: a network design problem for multicommodity flow
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Single-Sink Buy-at-Bulk LP Has Constant Integrality Gap
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On Rajagopalan and Vazirani's 3/2-approximation bound for the Iterated 1-Steiner heuristic
Information Processing Letters
Improved Combinatorial Algorithms for Facility Location Problems
SIAM Journal on Computing
An improved approximation algorithm for virtual private network design
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Tighter Bounds for Graph Steiner Tree Approximation
SIAM Journal on Discrete Mathematics
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
A polynomial-time approximation scheme for Steiner tree in planar graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
New Approaches for Virtual Private Network Design
SIAM Journal on Computing
Approximating connected facility location problems via random facility sampling and core detouring
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The Steiner tree problem on graphs: Inapproximability results
Theoretical Computer Science
Improved Approximation Algorithms for PRIZE-COLLECTING STEINER TREE and TSP
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
New geometry-inspired relaxations and algorithms for the metric steiner tree problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Connected facility location via random facility sampling and core detouring
Journal of Computer and System Sciences
A faster algorithm for the steiner tree problem
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Improved approximation for single-sink buy-at-bulk
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
On Steiner trees and minimum spanning trees in hypergraphs
Operations Research Letters
A polylogarithmic approximation for computing non-metric terminal Steiner trees
Information Processing Letters
Network design via core detouring for problems without a core
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Stackelberg strategies for network design games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
How well can primal-dual and local-ratio algorithms perform?
ACM Transactions on Algorithms (TALG)
Maximising lifetime for fault-tolerant target coverage in sensor networks
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
From Uncertainty to Nonlinearity: Solving Virtual Private Network via Single-Sink Buy-at-Bulk
Mathematics of Operations Research
On the low-dimensional steiner minimum tree problem in hamming metric
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Approximation algorithms for single and multi-commodity connected facility location
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Dealing with large hidden constants: engineering a planar steiner tree PTAS
Journal of Experimental Algorithmics (JEA)
An improved approximation algorithm for minimum-cost subset k-connectivity
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Primal-dual approximation algorithms for node-weighted steiner forest on planar graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded Treewidth
Journal of the ACM (JACM)
Improved approximation algorithms for Directed Steiner Forest
Journal of Computer and System Sciences
Strict Cost Sharing Schemes for Steiner Forest
SIAM Journal on Computing
Improved Approximation Algorithms for Prize-Collecting Steiner Tree and TSP
SIAM Journal on Computing
The entropy rounding method in approximation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximating fault-tolerant group-Steiner problems
Theoretical Computer Science
Prize-collecting Steiner problems on planar graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Preplanned restoration of multicast demands in optical networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Competitive and deterministic embeddings of virtual networks
ICDCN'12 Proceedings of the 13th international conference on Distributed Computing and Networking
Prize-Collecting steiner network problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Hypergraphic LP relaxations for steiner trees
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Fast local search for the steiner problem in graphs
Journal of Experimental Algorithmics (JEA)
Contraction-based steiner tree approximations in practice
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Optimal configuration of an optical network providing predefined multicast transmissions
Computer Networks: The International Journal of Computer and Telecommunications Networking
Matroids and integrality gaps for hypergraphic steiner tree relaxations
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Approximation algorithms for the maximum leaf spanning tree problem on acyclic digraphs
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Integrality gap of the hypergraphic relaxation of Steiner trees: A short proof of a 1.55 upper bound
Operations Research Letters
Minimum certificate dispersal with tree structures
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Node-weighted network design in planar and minor-closed families of graphs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
New advances in reoptimizing the minimum steiner tree problem
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Prize-collecting steiner network problems
ACM Transactions on Algorithms (TALG)
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
The internal Steiner tree problem: Hardness and approximations
Journal of Complexity
Primal-dual approximation algorithms for Node-Weighted Steiner Forest on planar graphs
Information and Computation
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 the approximability of Dense Steiner Problems
Journal of Discrete Algorithms
Competitive and deterministic embeddings of virtual networks
Theoretical Computer Science
Exponential approximation schemata for some network design problems
Journal of Discrete Algorithms
On the low-dimensional Steiner minimum tree problem in Hamming metric
Theoretical Computer Science
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The Steiner tree problem is one of the most fundamental NP-hard problems: given a weighted undirected graph and a subset of terminal nodes, find a minimum-cost tree spanning the terminals. In a sequence of papers, the approximation ratio for this problem was improved from 2 to the current best 1.55 [Robins,Zelikovsky-SIDMA'05]. All these algorithms are purely combinatorial. A long-standing open problem is whether there is an LP-relaxation for Steiner tree with integrality gap smaller than 2 [Vazirani,Rajagopalan-SODA'99]. In this paper we improve the approximation factor for Steiner tree, developing an LP-based approximation algorithm. Our algorithm is based on a, seemingly novel, iterative randomized rounding technique. We consider a directed-component cut relaxation for the k-restricted Steiner tree problem. We sample one of these components with probability proportional to the value of the associated variable in the optimal fractional solution and contract it. We iterate this process for a proper number of times and finally output the sampled components together with a minimum-cost terminal spanning tree in the remaining graph. Our algorithm delivers a solution of cost at most ln(4) times the cost of an optimal k-restricted Steiner tree. This directly implies a ln(4)+ε