Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of 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
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
Minimum Manhattan network is NP-complete
Proceedings of the twenty-fifth annual symposium on Computational geometry
A 1.5-approximation of the minimal manhattan network problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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Given a set of nodes in the plane and a constant t ≥ 1, a Euclidean t-spanner is a network in which, for any pair of nodes, the ratio of the network distance and the Euclidean distance of the two nodes is at most t. These networks have applications in transportation or communication network design and have been studied extensively. In this paper we study 1-spanners under the Manhattan (or L1-) metric. Such networks are called Manhattan networks. A Manhattan network for a set of nodes can be seen as a set of axis-parallel line segments whose union contains an x- and y-monotone path for each pair of nodes. It is not known whether it is NP-hard to compute minimum Manhattan networks, i.e. Manhattan networks of minimum total length. In this paper we present a factor-3 approximation algorithm for this problem. Given a set of n nodes, our algorithm takes O(n log n) time and linear space.