Distributed kinetic delaunay triangulation

Abstract

Delaunay triangulation is one of the most fundamental and well-studied topics in computational geometry. In particular, algorithms for constructing the Delaunay triangulation of moving points have also been proposed. However no previous work dealt with the Delaunay triangulation of moving points in distributed manner. This thesis proposes a distributed algorithm to maintain the Delaunay triangulation of moving points. We assume that every point is a processor which can only communicate with the adjacent points connected by edges in the Delaunay triangulation. The topological changes of the Delaunay triangulation due to the movement of the points are updated automatically by local operations of the points without any centralized processor or global information. In addition, we present an efficient method that balances the maintenance load for each point. Our algorithm can be applied to construct a scalable network.