New data structures for orthogonal range queries
SIAM Journal on Computing
Dynamic orthogonal segment intersection search
Journal of Algorithms
There are planar graphs almost as good as the complete graph
Journal of Computer and System Sciences
Delaunay graphs are almost as good as complete graphs
Discrete & Computational Geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
On sparse spanners of weighted graphs
Discrete & Computational Geometry
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Multidimensional divide-and-conquer
Communications of the ACM
Which Triangulations Approximate the Complete Graph?
Proceedings of the International Symposium on Optimal Algorithms
Approximating a minimum Manhattan network
Nordic Journal of Computing
A fast algorithm for approximating the detour of a polygonal chain
Computational Geometry: Theory and Applications
The Geometric Dilation of Finite Point Sets
Algorithmica
The minimum Manhattan network problem: approximations and exact solutions
Computational Geometry: Theory and Applications
Geometric Spanner Networks
On the geometric dilation of closed curves, graphs, and point sets
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum weight convex Steiner partitions
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D
Discrete & Computational Geometry
Sparse geometric graphs with small dilation
Computational Geometry: Theory and Applications
GD'12 Proceedings of the 20th international conference on Graph Drawing
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An orthogonal spanner network for a given set of n points in the plane is a plane straight line graph with axis-aligned edges that connects all input points. We show that for any set of n points in the plane, there is an orthogonal spanner network that (i) is short having a total edge length at most a constant times the length of a Euclidean minimum spanning tree for the point set; (ii) is small having O(n) vertices and edges; and (iii) has constant geometric dilation, which means that for any two points u and v in the network, the shortest path in the network between u and v is at most a constant times longer than the Euclidean distance between u and v. Such a network can be constructed in O(nlogn) time.