The steiner problem with edge lengths 1 and 2,
Information Processing Letters
The Steiner tree problem I: formulations, compositions and extension of facets
Mathematical Programming: Series A and B
The Steiner tree problem II: properties and classes of facets
Mathematical Programming: Series A and B
An improved approximation algorithm for multiway cut
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On the bidirected cut relaxation for the metric Steiner tree problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Equitable cost allocations via primal-dual-type algorithms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximation Hardness of the Steiner Tree Problem on Graphs
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
On Rajagopalan and Vazirani's 3/2-approximation bound for the Iterated 1-Steiner heuristic
Information Processing Letters
Tighter Bounds for Graph Steiner Tree Approximation
SIAM Journal on Discrete Mathematics
Approaches to the Steiner Problem in Networks
Algorithmics of Large and Complex Networks
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
How well can primal-dual and local-ratio algorithms perform?
ACM Transactions on Algorithms (TALG)
Hypergraphic LP relaxations for steiner trees
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Matroids and integrality gaps for hypergraphic steiner tree relaxations
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Steiner Tree Approximation via Iterative Randomized Rounding
Journal of the ACM (JACM)
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Determining the integrality gap of the bidirected cut relaxation for the metric Steiner tree problem, and exploiting it algorithmically, is a long-standing open problem. We use geometry to define an LP whose dual is equivalent to this relaxation. This opens up the possibility of using the primal-dual schema in a geometric setting for designing an algorithm for this problem. Using this approach, we obtain a 4/3 factor algorithm and integrality gap bound for the case of quasi-bipartite graphs; the previous best being 3/2 [RV99]. We also obtain a factor √2 strongly polynomial algorithm for this class of graphs. A key difficulty experienced by researchers in working with the bidirected cut relaxation was that any reasonable dual growth procedure produces extremely unwieldy dual solutions. A new algorithmic idea helps finesse this difficulty - that of reducing the cost of certain edges and constructing the dual in this altered instance - and this idea can be extracted into a new technique for running the primal-dual schema in the setting of approximation algorithms.