On Directed Steiner Trees (2002) [12 citations — 0 self]
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@INPROCEEDINGS{Zosin02ondirected,author = {Leonid Zosin and Samir Khuller},
title = {On Directed Steiner Trees},
booktitle = {In 13th Annual ACM-SIAM Symposium on Discrete Algorithms},
year = {2002},
pages = {59--63}
}
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Abstract:
The directed Steiner tree problem is the following: given a directed graph G = (V; E) with weights on the edges, a set of terminals S ` V, and a root vertex r, find a minimum weight out-branching T rooted at r, such that all vertices in S are included in T. This problem is known to be NPhard. Recently, non-trivial polynomial time approximation algorithms have been developed for this problem with worst case approximation guarantees of O(k ffl) for any fixed ffl? 0. We consider a natural LP relaxation of this problem. Using a dual formulation we construct a simple deterministic (D + 1)-approximation algorithm for a special case when the subgraph induced by V n S is a tree with depth D (for example, this can be shown to include the group Steiner tree problem as a special case, by the loss of poly-log factors in the approximation guarantee). We also show that this LP has an integrality gap of \Theta( p
Citations
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| 68 | Approximation algorithms for directed Steiner problems – Charikar, Chekuri, et al. - 1999 |
| 54 | Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median – Charikar, Chekuri, et al. - 1998 |
| 13 | A series of approximation algorithms for the Acyclic Directed Steiner Tree problem – Zelikovsky - 1997 |
| 1 | A polylogarithmic approximation for the group Steiner tree problem – Garg, Konjevod, et al. - 1998 |
