An augmenting path algorithm for linear matroid parity
Combinatorica
The steiner problem with edge lengths 1 and 2,
Information Processing Letters
An approximation algorithm for a bottleneck k-Steiner tree problem in the Euclidean plane
Information Processing Letters
Relay sensor placement in wireless sensor networks
Wireless Networks
On Exact Solutions to the Euclidean Bottleneck Steiner Tree Problem
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Exact Algorithms for the Bottleneck Steiner Tree Problem
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On exact solutions to the Euclidean bottleneck Steiner tree problem
Information Processing Letters
On the euclidean bottleneck full Steiner tree problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
The euclidean bottleneck steiner path problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
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A special case of the bottleneck Steiner tree problem in the Euclidean plane was considered in this paper. The problem has applications in the design of wireless communication networks, multifacility location, VLSI routing and network routing. For the special case which requires that there should be no edge connecting any two Steiner points in the optimal solution, a 3-restricted Steiner tree can be found indicating the existence of the performance ratio √2. In this paper, the special case of the problem is proved to be NP-hard and cannot be approximated within ratio √2. First a simple polynomial time approximation algorithm with performance ratio √3 is presented. Then based on this algorithm and the existence of the 3-restricted Steiner tree, a polynomial time approximation algorithm with performance ratio--√2 + ε is proposed, for any ε 0.