A new polynomial-time algorithm for linear programming
Combinatorica
On some distance problems in fixed orientations
SIAM Journal on Computing
Reducing the Steiner problem in a normal space
SIAM Journal on Computing
The shortest network under a given topology
Journal of Algorithms
On optimal interconnections
The Steiner tree problem in orientation metrics
Journal of Computer and System Sciences
Minimum Networks in Uniform Orientation Metrics
SIAM Journal on Computing
An Efficient Primal-Dual Interior-Point Method for Minimizing a Sum of Euclidean Norms
SIAM Journal on Scientific Computing
An Efficient Algorithm for Minimizing a Sum of Euclidean Norms with Applications
SIAM Journal on Optimization
An Efficient Algorithm for Minimizing a Sum of p-Norms
SIAM Journal on Optimization
The Steiner Minimal Tree Problem in the lambda-Geormetry Plane
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
An Efficient Newton Barrier Method for Minimizing a Sum of Euclidean Norms
An Efficient Newton Barrier Method for Minimizing a Sum of Euclidean Norms
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A polynomial time dual algorithm for the Euclidean multifacility location problem
Operations Research Letters
Comment on "Computing the Shortest Network under a Fixed Topology'
IEEE Transactions on Computers
Steiner trees for fixed orientation metrics
Journal of Global Optimization
| Hi-index | 14.98 |
We show that, in any given uniform orientation metric plane, the shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations. When the given topology is restricted to a Steiner topology, our result implies that the Steiner minimum tree under a given Steiner topology can be computed in polynomial time in any given uniform orientation metric with $\big. \lambda\bigr.$ legal orientations for any fixed integer $\big. \lambda \ge 2\bigr.$. This settles an open problem posed in a recent paper [3].