Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A Fast Heuristic for Approximating the Minimum Weight Triangulation (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Picking alignments from (steiner) trees
Proceedings of the sixth annual international conference on Computational biology
Placing an abnoxious facility in geometric networks
Nordic Journal of Computing
The minimum Manhattan network problem: approximations and exact solutions
Computational Geometry: Theory and Applications
A rounding algorithm for approximating minimum Manhattan networks
Theoretical Computer Science
Light orthogonal networks with constant geometric dilation
Journal of Discrete Algorithms
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 minimum Manhattan network problem: Approximations and exact solutions
Computational Geometry: Theory and Applications
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
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
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Given a set S of n points in the plane, we define a Manhattan Network on S as a rectilinear network G with the property that for every pair of points in S, the network G contains the shortest rectilinear path between them. A Minimum Manhattan Network on S is a Manhattan network of minimum possible length. A Manhattan network can be thought of as a graph G=(V,E), where the vertex set V corresponds to points from S and a set of Steiner points S', and the edges in E correspond to horizontal or vertical line segments connecting points in S U S'. A Manhattan network can also be thought of as a 1-spanner (for the L1-metric) for the points in S.Let R be an algorithm that produces a rectangulation of a staircase polygon in time R(n) of weight at most r times the optimal. We design an O(n\log n + R(n)) time algorithm which, given a set S of n points in the plane, produces a Manhattan network on S with total weight at most 4r times that of a minimum Manhattan network. Using known rectangulation algorithms, this gives us an O(n3)-time algorithm with approximation factor four, and an O(n \log n)-time algorithm with approximation factor eight.