A data structure for bicategories, with application to speeding up an approximation algorithm
Information Processing Letters
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
The prize collecting Steiner tree problem: theory and practice
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A faster implementation of the Goemans-Williamson clustering algorithm
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximate k-MSTs and k-Steiner trees via the primal-dual method and Lagrangean relaxation
Mathematical Programming: Series A and B
Efficient algorithms for the prize collecting Steiner tree problems with interval data
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
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The primal-dual scheme has been used to provide approximation algorithms for many problems. Goemans and Williamson gave a (2-1/(n-1))-approximation for the Prize-Collecting Steiner Tree Problem that runs in O(n^3logn) time-it applies the primal-dual scheme once for each of the n vertices of the graph. We present a primal-dual algorithm that runs in O(n^2logn), as it applies this scheme only once, and achieves the slightly better ratio of (2-2/n). We also show a tight example for the analysis of the algorithm and discuss briefly a couple of other algorithms described in the literature.