Searching for the kernel of a polygon—a competitive strategy
Proceedings of the eleventh annual symposium on Computational geometry
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
A Fast Algorithm for Approximating the Detour of a Polygonal Chain
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Approximation algorithms for the bottleneck stretch factor problem
Nordic Journal of Computing
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Finding the best shortcut in a geometric network
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Computational Geometry: Theory and Applications
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)
Geometric dilation of closed planar curves: New lower bounds
Computational Geometry: Theory and Applications
Feed-links for network extensions
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Algorithms for graphs of bounded treewidth via orthogonal range searching
Computational Geometry: Theory and Applications
Connect the Dot: Computing Feed-Links with Minimum Dilation
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Light orthogonal networks with constant geometric dilation
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Dilation-optimal edge deletion in polygonal cycles
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Almost all Delaunay triangulations have stretch factor greater than π/2
Computational Geometry: Theory and Applications
Exact and approximation algorithms for computing the dilation spectrum of paths, trees, and cycles
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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The maximum detour and spanning ratio of an embedded graph G are values that measure how well G approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe O(n log n) time algorithms for computing the maximum detour and spanning ratio of a planar polygonal path. These algorithms solve open problems posed in at least two previous works [5,10]. We also generalize these algorithms to obtain O(n log2 n) time algorithms for computing the maximum detour and spanning ratio of planar trees and cycles.