Data structures and network algorithms
Data structures and network algorithms
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
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
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Data structures for mobile data
Journal of Algorithms
Voronoi Diagrams of Moving Points in the Plane
WG '91 Proceedings of the 17th International Workshop
Kinetic collision detection between two simple polygons
Computational Geometry: Theory and Applications
A Two-Dimensional Kinetic Triangulation with Near-Quadratic Topological Changes
Discrete & Computational Geometry
Triangulations and Applications (Mathematics and Visualization)
Triangulations and Applications (Mathematics and Visualization)
Kinetic and dynamic data structures for convex hulls and upper envelopes
Computational Geometry: Theory and Applications
Kinetic and dynamic data structures for closest pair and all nearest neighbors
ACM Transactions on Algorithms (TALG)
Kinetic stable Delaunay graphs
Proceedings of the twenty-sixth annual symposium on Computational geometry
On topological changes in the delaunay triangulation of moving points
Proceedings of the twenty-eighth annual symposium on Computational geometry
Kinetic pie delaunay graph and its applications
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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We present a simple randomized scheme for triangulating a set P of n points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of P move continuously along piecewise algebraic trajectories of constant description complexity. Our triangulation scheme experiences an expected number of O(n^2@b"s"+"2(n)log^2n) discrete changes, and handles them in a manner that satisfies all the standard requirements from a kinetic data structure: compactness, efficiency, locality and responsiveness. Here s is the maximum number of times at which any specific triple of points of P can become collinear, @b"s"+"2(q)=@l"s"+"2(q)/q, and @l"s"+"2(q) is the maximum length of Davenport-Schinzel sequences of order s+2 on q symbols. Thus, compared to the previous solution of Agarwal, Wang and Yu (2006) [4], we achieve a (slightly) improved bound on the number of discrete changes in the triangulation. In addition, we believe that our scheme is conceptually simpler, and easier to implement and analyze.