Straight-Path Queries in Trajectory Data

Inspired by sports analysis, we study data structures for storing a trajectory representing the movement of a player during a game, such that the following queries can be answered: Given two positions s and t, report all sub-trajectories in which the player moved in a more or less straight line from s to t. We consider two measures of straightness, namely dilation and direction deviation, and present efficient construction algorithms for our data structures, and analyze their performance. We also present an O(n) algorithm that, given a trajectory P and a threshold τ , finds a simplification of P with a minimum number of vertices such that each edge in the simplification replaces a sub-trajectory of length at most τ times the length of the edge. This significantly improves the fastest known algorithm for the problem.