Ordered polyline trees for efficient search of objects moving on a graph

Abstract

We discuss a spatio-temporal data structure to index objects moving on a graph. It is designed to efficiently answer rectangle R plus time instance and time interval queries about the past positions of moving objects. Such data structures are useful, for example, when searching which vehicles moving on a road network in specific areas at specific times. Unlike other data structures that use R-trees to index bounding boxes of moving object trajectories, our data structure indexes oriented line segments representing positions of moving objects at different times. For n moving object instances (unique entries of moving objects) on a graph with E edges, we show that O(log2E + |L|log22(n/E) + k) time is required to answer a rectangle R plus time interval query, for |L| the number of edges intersected by R and k the number of line segments containing moving object instances in range. Space O(n2/E + E) is required in the worst case to store n moving object instances in E ordered polyline trees. Space Ω(n + E) is required to store the history of all n moving object instances. © 2010 Springer-Verlag Berlin Heidelberg.