The steiner problem with edge lengths 1 and 2,
Information Processing Letters
Improved approximations for the Steiner tree problem
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Computing
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The Steiner ratio of several discrete metric spaces
Discrete Mathematics
On the Approximability of the Steiner Tree Problem in Phylogeny
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Computing steiner minimum trees in Hamming metric
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
Hi-index | 5.23 |
While it is known that the d-dimensional Steiner minimum tree problem in Hamming metric is NP-complete if d is part of the input, it is an open question whether this also holds for fixed dimensions. In this paper, this question is answered by showing that the Steiner minimum tree problem in Hamming metric is already NP-complete in 3 dimensions. Furthermore, we show that, the minimum spanning tree gives a 2-2d approximation on the Steiner minimum tree for d=2. Using this result, we analyse the so-called k-LCA and A"k approximation algorithms and show improved approximation guarantees for low dimensions.