This paper presents simple kinetic data structures (KDSs) for solutions to some fundamental proximity problems, namely, the all nearest neighbors problem, the closest pair problem, and the Euclidean minimum spanning tree.Expand

This paper presents a kinetic data structure (KDS) for maintenance of the Euclidean minimum spanning tree (EMST) on a set of moving points in 2-dimensional space by which the EMST is maintained efficiently during the motion.Expand

We construct a new proximity graph, called the Pie Delaunay graph, on a set of n points which is a super graph of Yaograph and Euclidean minimum spanning tree (EMST).Expand

We present an O ź ( n 5 / 3 ) -time algorithm1 to compute a ( 1 + ź ) -factor approximation to the minimum closest pair distance over time, for any constant ź 0 and any constant dimension d.Expand

We investigate a kinetic version of point-set embeddability. Given a plane graph G(V,E) where |V|=n, and a set P of n moving points where the trajectory of each point is an algebraic function of… Expand

This paper presents kinetic data structures (KDS’s) for maintaining the Semi-Yao graph, all the nearest neighbors, and all the (1 + )-nearest neighbors of a set of moving points in R.Expand

This paper presents a simple kinetic data structure for maintaining the edges of the Semi-Yao graph, a sparse graph whose edge set includes the pairs of nearest neighbors as a subset.Expand