Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Near-quadratic bounds for the L1 Voronoi diagram of moving points
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and 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
Algorithmic issues in modeling motion
ACM Computing Surveys (CSUR)
Maintaining deforming surface meshes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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A triangulation of a set S of points in the plane is a subdivision of the convex hull of S into triangles whose vertices are points of S. Given a set S of n points in ℝ3, each moving independently, we wish to maintain a triangulation of S. The triangulation needs to be updated periodically as the points in S move, so the goal is to maintain a triangulation with small number of topological events, each being the insertion or deletion of an edge. We propose a kinetic data structure (KDS) that processes n2 2O(√log n•log log n ) topological events, with high probability, if the trajectories of input points are algebraic curves of fixed degree. Each topological event can be processed in O(log n) time. This is the first known KDS for maintaining a triangulation that processes near-quadratic number of topological events, and almost matches the Ω(n2) lower bound, [1]. The number of topological events can be reduced to nk • 2O(√log k•log log n ) if only K of the points are moving.