An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Optimal point placement for mesh smoothing
Journal of Algorithms
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
An optimal randomized algorithm for maximum Tukey depth
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Finding the best shortcut in a geometric network
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Embedding ultrametrics into low-dimensional spaces
Proceedings of the twenty-second annual symposium on Computational geometry
The density of iterated crossing points and a gap result for triangulations of finite point sets
Proceedings of the twenty-second annual symposium on Computational geometry
Sparse geometric graphs with small dilation
Computational Geometry: Theory and Applications
Optimal location of transportation devices
Computational Geometry: Theory and Applications
Computing geometric minimum-dilation graphs is NP-hard
GD'06 Proceedings of the 14th international conference on Graph drawing
Approximate weighted farthest neighbors and minimum dilation stars
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Sparse geometric graphs with small dilation
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Approximated algorithms for the minimum dilation triangulation problem
Journal of Heuristics
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The dilation of a Euclidean graph is defined as the ratio of distance in the graph divided by distance in Rd. In this paper we consider the problem of positioning the root of a star such that the dilation of the resulting star is minimal. We present a deterministic O(n log n)-time algorithm for evaluating the dilation of a given star; a randomized O(n log n) expected-time algorithm for finding an optimal center in Rd; and for the case d = 2, a randomized O(n2α(n) log2n) expected-time algorithm for finding an optimal center among the input points.