A general approximation technique for constrained forest problems
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
A primal-dual approximation algorithm for the Steiner forest problem
Information Processing Letters
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
A polylogarithmic approximation algorithm for the group Steiner tree problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A 2 + ε approximation algorithm for the k-MST problem
SODA '00 Proceedings of the eleventh 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
Approximation Hardness of the Steiner Tree Problem on Graphs
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
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We study the approximation complexity of the @e-Dense Steiner Tree Problem which was introduced by Karpinski and Zelikovsky (1998) [13]. They proved that for each @e0, this problem admits a PTAS. Based on their method we consider here dense versions of various Steiner Tree problems. In particular, we give polynomial time approximation schemes for the @e-Dense k-Steiner Tree Problem, the @e-Dense Prize Collecting Steiner Tree Problem and the @e-Dense Group Steiner Tree Problem. We also show that the @e-Dense Steiner Forest Problem is approximable within ratio 1+O((@?"ilog|S"i|)/(@?"i|S"i|)) where S"1,...,S"n are the terminal sets of the given instance. This ratio becomes small when the number of terminal sets is small compared to the total number of terminals.