On sparse spanners of weighted graphs
Discrete & Computational Geometry
Lower bounds for computing geometric spanners and approximate shortest paths
Discrete Applied Mathematics
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
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
A rounding algorithm for approximating minimum Manhattan networks
Theoretical Computer Science
The minimum Manhattan network problem: Approximations and exact solutions
Computational Geometry: Theory and Applications
A 1.5-approximation of the minimal manhattan network problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Approximating minimum manhattan networks in higher dimensions
ESA'11 Proceedings of the 19th European conference on Algorithms
| Hi-index | 0.00 |
For the Minimal Manhattan Network Problem in three dimensions (MMN3D), one is given a set of points in space, and an admissible solution is an axis-parallel network that connects every pair of points by a shortest path under L 1-norm (Manhattan metric). The goal is to minimize the overall length of the network. Here, we show that MMN3D is $\cal NP$- and $\cal APX$-hard, with a lower bound on the approximability of 1 + 2·10− 5. This lower bound applies to MMN2-3D already, a sub-problem in between the two and three dimensional case. For MMN2-3D, we also develop a 3-approximation algorithm which is the first algorithm for the Minimal Manhattan Network Problem in three dimensions at all.