Range Reporting for Moving Points on a Grid

In this paper we describe a new data structure that supports orthogonal range reporting queries on a set of points that move along linear trajectories on a U × U grid. The assumption that points lie on a U × U grid enables us to significantly decrease the query time in comparison to the standard kinetic model. Our data structure answers queries in O( √ logU/ log logU + k) time, where k denotes the number of points in the answer. The above improves over the Ω(log n) lower bound that is valid in the infinite-precision kinetic model. The methods used in this paper could be also of independent interest.