Center and diameter problems in plane triangulations and quadrangulations
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Diameters, centers, and approximating trees of delta-hyperbolicgeodesic spaces and graphs
Proceedings of the twenty-fourth annual symposium on Computational geometry
Algorithms and theory of computation handbook
The geodesic diameter of polygonal domains
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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We present an O(n) time algorithm for computing row-wise maxima or minima of an implicit, totally monotone $n \times n$ matrix whose entries represent shortest-path distances between pairs of vertices in a simple polygon. We apply this result to derive improved algorithms for several well-known problems in computational geometry. Most prominently, we obtain linear-time algorithms for computing the geodesic diameter, all farthest neighbors, and external farthest neighbors of a simple polygon, improving the previous best result by a factor of O(log n) in each case.