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
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh 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
Steiner trees in uniformly quasi-bipartite graphs
Information Processing Letters
The Single-Sink Buy-at-Bulk LP Has Constant Integrality Gap
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
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
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
New Approaches for Virtual Private Network Design
SIAM Journal on Computing
The Steiner tree problem on graphs: Inapproximability results
Theoretical Computer Science
Improved approximation algorithms for the single-sink buy-at-bulk network design problems
Journal of Discrete Algorithms
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
An O(n log n) approximation scheme for Steiner tree in planar graphs
ACM Transactions on Algorithms (TALG)
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 partition-based relaxation for Steiner trees
Mathematical Programming: Series A and B
From Uncertainty to Nonlinearity: Solving Virtual Private Network via Single-Sink Buy-at-Bulk
Mathematics of Operations Research
Approximation algorithms for single and multi-commodity connected facility location
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Improved Approximation Algorithms for Prize-Collecting Steiner Tree and TSP
SIAM Journal on Computing
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
Hypergraphic LP relaxations for steiner trees
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Integrality gap of the hypergraphic relaxation of Steiner trees: A short proof of a 1.55 upper bound
Operations Research Letters
On Steiner trees and minimum spanning trees in hypergraphs
Operations Research Letters
Matroids and integrality gaps for hypergraphic steiner tree relaxations
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Guest column: the elusive inapproximability of the TSP
ACM SIGACT News
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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 1.55 [Robins and Zelikovsky 2005]. All these algorithms are purely combinatorial. A long-standing open problem is whether there is an LP relaxation of Steiner tree with integrality gap smaller than 2 [Rajagopalan and Vazirani 1999]. In this article we present an LP-based approximation algorithm for Steiner tree with an improved approximation factor. Our algorithm is based on a, seemingly novel, iterative randomized rounding technique. We consider an LP relaxation of the problem, which is based on the notion of directed components. We sample one component with probability proportional to the value of the associated variable in a fractional solution: the sampled component is contracted and the LP is updated consequently. We iterate this process until all terminals are connected. Our algorithm delivers a solution of cost at most ln(4) + ϵ As a by-product of our analysis, we show that the integrality gap of our LP is at most 1.55, hence answering the mentioned open question.