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, we present efficient construction algorithms for our data structures, and we analyze their performance. We also present an O(n1.5+ε) algorithm for the following simplification problem: given a trajectory P and a threshold τ, find a simplification of P with a minimum number of vertices such that each edge in the simplification replaces a sub-trajectory whose length is at most τ times the length of the edge. This significantly improves the fastest known algorithm for the problem.