On a multidimensional search technique and its application to the Euclidean one centre problem
SIAM Journal on Computing
Discrete Mathematics
Computing the link center of a simple polygon
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
Computing the geodesic center of a simple polygon
Discrete & Computational Geometry
Computing geodesic furthest neighbors in simple polygons
Journal of Computer and System Sciences
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Computational Geometry: Theory and Applications
An O(n log n) algorithm for computing the link center of a simple polygon
Discrete & Computational Geometry
An optimal algorithm for the rectilinear link center of a rectilinear polygon
Computational Geometry: Theory and Applications
Matrix Searching with the Shortest-Path Metric
SIAM Journal on Computing
Distance approximating trees for chordal and dually chordal graphs
Journal of Algorithms
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
Regular Article: Graphs of Some CAT(0) Complexes
Advances in Applied Mathematics
A note on distance approximating trees in graphs
European Journal of Combinatorics
Diameter determination on restricted graph families
Discrete Applied Mathematics
Center and diameter problems in plane triangulations and quadrangulations
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
European Journal of Combinatorics
SIAM Journal on Discrete Mathematics
A Linear-Time Algorithm for Finding a Central Vertex of a Chordal Graph
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Algorithms on negatively curved spaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Efficient algorithms for center problems in cactus networks
Theoretical Computer Science
Discrete & Computational Geometry
Squarepants in a tree: sum of subtree clustering and hyperbolic pants decomposition
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Packing and Covering δ-Hyperbolic Spaces by Balls
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Horoball hulls and extents in positive definite space
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Cop and Robber Games When the Robber Can Hide and Ride
SIAM Journal on Discrete Mathematics
On computing the diameter of real-world directed (weighted) graphs
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
On computing the diameter of real-world undirected graphs
Theoretical Computer Science
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δ-Hyperbolic metric spaces have been defined by M. Gromov via a simple 4-point condition: for any four points u,v,w,x, the two larger of the sums d(u,v)+d(w,x), d(u,w)+d(v,x), d(u,x)+d(v,w) differ by at most 2δ. Given a finite set S of points of a δ-hyperbolic space, we present simple and fast methods for approximating the diameter of S with an additive error 2δ and computing an approximate radius and center of a smallest enclosing ball for S with an additive error 3δ. These algorithms run in linear time for classical hyperbolic spaces and for δ-hyperbolic graphs and networks. Furthermore, we show that for δ-hyperbolic graphs G=(V,E) with uniformly bounded degrees of vertices, the exact center of S can be computed in linear time O(|E|). We also provide a simple construction of distance approximating trees of δ-hyperbolic graphs G on n vertices with an additive error O(δlog2 n). This construction has an additive error comparable with that given by Gromov for n-point δ-hyperbolic spaces, but can be implemented in O(|E|) time (instead of O(n2)). Finally, we establish that several geometrical classes of graphs have bounded hyperbolicity.