## 30 Citations

### Fast Approximation Algorithm for Restricted Euclidean Bottleneck Steiner Tree Problem

- Computer ScienceJ. Multim.
- 2014

It is shown that the bottleneck Steiner tree problem is NP-hard and cannot be approximated within unless P=NP, and a fast polynomial time deterministic approximation algorithm with performance ratio is provided.

### Exact Algorithms for the Bottleneck Steiner Tree

- Computer Science, Mathematics
- 2009

This paper presents the first fixed-parameter tractable al- gorithm running in O(f(k) · n 2 log n) time for the L1 and the L∞ metrics, and the first exact algorithm for any other Lp metric with 1 <p< ∞ whose time complexity is O( f( k) ·(n k +nlog n)) ,w heref(K) is a function dependent only on k.

### Exact Algorithms for the Bottleneck Steiner Tree Problem

- Computer Science, MathematicsAlgorithmica
- 2011

This paper presents the first fixed-parameter tractable algorithm running in f(k)⋅nlog 2n time for the L1 and the L∞ metrics, and the first exact algorithm for theLp metric for any fixed rational p with 1<p<∞ whose time complexity is f( k) ⋅(nk+nlog n), where f(K) is a function dependent only on k.

### Nearly Optimal Solution for Restricted Euclidean Bottleneck Steiner Tree Problem

- Computer Science, MathematicsJ. Networks
- 2014

A restricted version of the bottleneck Steiner tree problem in the Euclidean plane which requires that only degree-2 Steiner points are possibly adjacent in the optimal solution is studied.

### On the euclidean bottleneck full Steiner tree problem

- Computer Science, MathematicsSoCG '11
- 2011

This paper presents an exact algorithm of O((n+m)log2m) time to solve the BFST problem and shows that the k-BFST problem is NP-hard and that there exists a polynomial-time approximation algorithm for the problem with performance ratio 4.

### Generalised k-Steiner Tree Problems in Normed Planes

- MathematicsAlgorithmica
- 2013

This paper generalises Georgakopoulos and Papadimitriou's approach in order to solve the k-Steiner tree problem, in which the Steiner minimum tree may contain up to k Steiner points for a given constant k, and shows that, for any fixed k, such problems can be solved in O(n2k) time.

### The euclidean bottleneck steiner path problem

- Computer ScienceSoCG '11
- 2011

An O(n log<sup>2</sup> n)-time algorithm that computes an optimal solution, for any constant k, based on two new geometric structures that are based on an (α,β)-pair decomposition of P and a floor (1+ε)-spanner of P.

### The Euclidean Bottleneck Full Steiner Tree Problem

- Computer Science, MathematicsAlgorithmica
- 2013

It is shown that the k-BFST problem is NP-hard and that there exists a polynomial-time approximation algorithm for the problem with performance ratio 4.5 and an exact algorithm of ${{{\mathcal {O}}}}((n+m)\log^{2}{m})$ time to solve the BFST problem.

### An exact algorithm for the bottleneck 2-connected k-Steiner network problem in Lp planes

- MathematicsDiscret. Appl. Math.
- 2016

## References

SHOWING 1-10 OF 17 REFERENCES

### Exact Algorithms for the Bottleneck Steiner Tree Problem

- Computer Science, MathematicsAlgorithmica
- 2011

This paper presents the first fixed-parameter tractable algorithm running in f(k)⋅nlog 2n time for the L1 and the L∞ metrics, and the first exact algorithm for theLp metric for any fixed rational p with 1<p<∞ whose time complexity is f( k) ⋅(nk+nlog n), where f(K) is a function dependent only on k.

### Approximation algorithm for bottleneck Steiner tree problem in the Euclidean plane

- Computer ScienceJournal of Computer Science and Technology
- 2008

The special case of the bottleneck Steiner tree problem in the Euclidean plane is proved to beNP-hard and cannot be approximated within ratio √2.

### Optimal and approximate bottleneck Steiner trees

- Computer ScienceOper. Res. Lett.
- 1996

### An approximation algorithm for a bottleneck k-Steiner tree problem in the Euclidean plane

- Mathematics, Computer ScienceInf. Process. Lett.
- 2002

### Bottleneck Steiner Trees in the Plane

- Computer ScienceIEEE Trans. Computers
- 1992

It is shown that when locations of Steiner points are not fixed the problem remains NP-complete; however, if the topology of the final tree is given, then the problem can be solved in Theta ( mod rho mod log mod r ho mod ) time.

### Approximations for a Bottleneck Steiner Tree Problem

- MathematicsAlgorithmica
- 2001

It is shown that if NP is NP-hard, then there exists a polynomial-time approximation with performance ratio 2 for the problem in both the rectilinear plane and the Euclidean plane.

### On Two Geometric Problems Related to the Traveling Salesman Problem

- Computer ScienceJ. Algorithms
- 1984

### A powerful global router: based on Steiner min-max trees

- Computer Science1989 IEEE International Conference on Computer-Aided Design. Digest of Technical Papers
- 1989

A study is made of the global routing of multiterminal nets, and an efficient algorithm is presented for obtaining a Steiner min-max tree, in a weighted graph.

### The Farthest Color Voronoi Diagram and Related Problems

- Computer Science
- 2001

This paper provides algorithms that may help to achieve this goal for various specifications of the term “neighborhood” for various types of facilities modeled by n colored points in the plane, each type by its own color.

### The upper envelope of voronoi surfaces and its applications

- MathematicsSCG '91
- 1991

Borders on the number of vertices on the upper envelope of a collection of Voronoi surfaces are derived, and efficient algorithms to calculate these vertices are provided.