A faster approximation algorithm for the Steiner problem in graphs
Information Processing Letters
Introduction to algorithms
Steiner's problem in graphs: heuristic methods
Discrete Applied Mathematics - Special issue: combinatorial methods in VLSI
Survivable networks, linear programming relaxations and the parsimonious property
Mathematical Programming: Series A and B
The Steiner tree problem I: formulations, compositions and extension of facets
Mathematical Programming: Series A and B
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
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
On the bidirected cut relaxation for the metric Steiner tree problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
New primal-dual algorithms for Steiner tree problems
Computers and Operations Research
Approaches to the Steiner Problem in Networks
Algorithmics of Large and Complex Networks
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Contraction-based steiner tree approximations in practice
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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We study several old and new algorithms for computing lower and upper bounds for the Steiner problem in networks using dual-ascent and primal-dual strategies. We show that none of the known algorithms can both generate tight lower bounds empirically and guarantee their quality theoretically; and we present a new algorithm which combines both features. The new algorithm has running time O(re log n) and guarantees a ratio of at most two between the generated upper and lower bounds, whereas the fastest previous algorithm with comparably tight empirical bounds has running time O(e2) without a constant approximation ratio. Furthermore, we show that the approximation ratio two between the bounds can even be achieved in time O(e + n log n), improving the previous time bound of O(n2 log n).