Math @ Duke

Publications [#235616] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Wang, Y; Yu, H, A 2D kinetic triangulation with nearquadratic topological changes,
Proceedings of the Annual Symposium on Computational Geometry
(2004),
pp. 180189
(last updated on 2018/11/20)
Abstract: 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 ℝ2, 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 n22O(√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 nearquadratic 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.


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