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
The minimum manhattan network problem: a fast factor-3 approximation
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
A rounding algorithm for approximating minimum Manhattan networks
Theoretical Computer Science
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
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Given a set of points in the plane, the Minimal Manhattan Network Problem asks for an axis-parallel network that connects every pair of points by a shortest path under L1-norm (Manhattan metric). The goal is to minimize the overall length of the network. We present an approximation algorithm that provides a solution of length at most 1.5 times the optimum. Previously, the best known algorithm has given only a 2-approximation.