An Efficient Kinetic Range Query for One Dimensional Axis Parallel Segments

Abstract

We present a kinetic data structure named Kinetic Interval Graph (KI-Graph) for performing efficient range search on moving one dimensional axis-parallel segments. This finds applications in Artificial Intelligence such as robotic motion. The structure requires O(n) storage. The time taken per update when a critical event occurs is O (1) thereby improving responsiveness when compared to the kinetic segment trees, while the overall updates across all segments at a time instance is at most n/2. Also, range query is performed efficiently in θ (k) time, where k segments are reported.