Bottleneck Steiner Trees in the Plane
IEEE Transactions on Computers
Improved approximations for the Steiner tree problem
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Computing
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
A 1.598 approximation algorithm for the Steiner problem in graphs
Proceedings of the tenth 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
An approximation algorithm for a bottleneck k-Steiner tree problem in the Euclidean plane
Information Processing Letters
On the terminal Steiner tree problem
Information Processing Letters
Theoretical Computer Science
Approximation algorithm for bottleneck steiner tree problem in the euclidean plane
Journal of Computer Science and Technology
Algorithms for terminal Steiner trees
Theoretical Computer Science
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
On the full and bottleneck full Steiner tree problems
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
On exact solutions to the Euclidean bottleneck Steiner tree problem
Information Processing Letters
An optimal algorithm for the Euclidean bottleneck full Steiner tree problem
Computational Geometry: Theory and Applications
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Given two sets in the plane, R of n (terminal) points and S of m (Steiner) points, a full Steiner tree is a Steiner tree in which all points of R are leaves. In the bottleneck full Steiner tree (BFST) problem, one has to find a full Steiner tree T (with any number of Steiner points from S), such that the length of the longest edge in T is minimized, and, in the k-BFST problem, has to find a full Steiner tree T with at most k ≤ m Steiner points from S such that the length of the longest edge in T is minimized. The problems are motivated by wireless network design. In this paper, we present an exact algorithm of O((n+m)log2m) time to solve the BFST problem. Moreover, we show that the k-BFST problem is NP-hard and that there exists a polynomial-time approximation algorithm for the problem with performance ratio 4.