A 2D kinetic triangulation with near-quadratic topological changes

Given a set of n points S in the plane, a triangulation of S is a subdivision of the convex hull into triangles whose vertices are from S. In the kinetic setting, the input point set is replaced by a continuous family S(t) indexed by time t. We wish to maintain a triangulation for S(t) with small number of topological events, i.e., small number of changes (such as insertion or deletion of an edge) to the triangulation through time. In particular, we propose a kinetic data structure (KDS) that processes O(n2 2O( √ log n·log log n) ) topological events with high probability if the trajectories of input points are algebraic curves of fixed degree. The total time for maintaining this triangulation using KDS is of roughly the same order. Our algorithm relies on a hierarchical fan triangulation that we propose, which is built based upon a randomized hierarchical scheme. This is the first known KDS for maintaining a triangulation that processes near-quadratic events. It improves over th...

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: Pankaj K. Agarwal, Yusu Wang, Hai Yu
• Keywords: COMPGEOM 2004, Input Points, Kinetic Data Structures, Triangulation