Kinetic data structures for all nearest neighbors and closest pair in the plane
Zahed Rahmati, Valerie Jean King, Sue H. Whitesides · 2013
This paper presents a kinetic data structure (KDS) for solutions to the all nearest neighbors problem and the closest pair problem in the plane. For a set P of n moving points where the trajectory of each point is an algebraic function of constant maximum degree s, our kinetic algorithm uses O(n) space and O(n log n) preprocessing time, and processes O(n2β22s+2(n)log n) events with total processing time O(n2β22s+2(n)log2 n), where βs(n) is an extremely slow-growing function. In terms of the KDS performance criteria, our KDS is efficient, responsive (in an amortized sense), and compact.