A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
Approximation algorithms
An Improved Algorithm for the Minimum Manhattan Network Problem
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Approximating a minimum Manhattan network
Nordic Journal of Computing
The minimum Manhattan network problem: approximations and exact solutions
Computational Geometry: Theory and Applications
Geometric Spanner Networks
The minimum manhattan network problem: a fast factor-3 approximation
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
A 1.5-approximation of the minimal manhattan network problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A Fast 2-Approximation Algorithm for the Minimum Manhattan Network Problem
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
The Minimal Manhattan Network Problem in Three Dimensions
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Minimum Manhattan network is NP-complete
Proceedings of the twenty-fifth annual symposium on Computational geometry
The Transitive Minimum Manhattan Subnetwork Problem in 3 dimensions
Discrete Applied Mathematics
Approximating minimum manhattan networks in higher dimensions
ESA'11 Proceedings of the 19th European conference on Algorithms
| Hi-index | 5.23 |
For a set T of n points (terminals) in the plane, a Manhattan network on T is a network N(T)=(V,E) with the property that its edges are horizontal or vertical segments connecting points in V@?T and for every pair of terminals, the network N(T) contains a shortest l"1-path between them. A minimum Manhattan network on T is a Manhattan network of minimum possible length. The problem of finding minimum Manhattan networks has been introduced by Gudmundsson, Levcopoulos, and Narasimhan [J. Gudmundsson, C. Levcopoulos, G. Narasimhan, Approximating a minimum Manhattan network, Nordic Journal of Computing 8 (2001) 219-232. Proc. APPROX'99, 1999, pp. 28-37] and its complexity status is unknown. Several approximation algorithms (with factors 8, 4, and 3) have been proposed; recently Kato, Imai, and Asano [R. Kato, K. Imai, T. Asano, An improved algorithm for the minimum Manhattan network problem, ISAAC'02, in: LNCS, vol. 2518, 2002, pp. 344-356] have given a factor 2-approximation algorithm, however their correctness proof is incomplete. In this paper, we propose a rounding 2-approximation algorithm based on an LP-formulation of the minimum Manhattan network problem.