Efficient Compression and Indexing of Trajectories

Abstract

We present a new compressed representation of free trajectories of moving objects. It combines a partial-sums-based structure that retrieves in constant time the position of the object at any instant, with a hierarchical minimum-bounding-boxes representation that allows determining if the object is seen in a certain rectangular area during a time period. Combined with spatial snapshots at regular intervals, the representation is shown to outperform classical ones by orders of magnitude in space, and also to outperform previous compressed representations in time performance, when using the same amount of space.

Funded in part by European Union Horizon 2020 Marie Skłodowska-Curie grant agreement No. 690941; MINECO (PGE and FEDER) [TIN2016-78011-C4-1-R;TIN2013-46238-C4-3-R]; CDTI, MINECO [ITC-20161074;IDI-20141259;ITC-20151305;ITC-20151247]; Xunta de Galicia (co-founded with FEDER) [ED431G/01]; and Fondecyt Grants 1-171058 and 1-170048, Chile.

A Dataset Details

The dataset used in our experimental evaluation corresponds to a real dataset storing the movements of 3,654 boats sailing in the UTM Zone 10 during one month of 2014. It was obtained from MarineCadastre.¹ Every position emitted by a ship is discretized into a matrix where the cell size is $50 \times 50$ meters. With this data normalization, we obtain a matrix with 1,001,451,325 cells, 2,723 in the x-axis and 367,775 in the y-axis. As our structure needs the position of the objects at regular timestamps, we preprocessed the signals every minute, sampling the time into 44,642 min in one month.

To filter out some obvious GPS errors, we set the maximum speed of our dataset to 55 cells per minute (over 234 km/h) and deleted every movement faster than this speed. In addition, we observe that most of the boats sent their positions frequently when they were moving, but not when they were stopped or moving slowly. This produced logs of boats with many small periods without signals (absence period). Taking into account that an object cannot move too far away during a small interval of time, we interpolated the signals when the absence period was smaller than 15 min, filling the periods of absence with these interpolated positions.

With these settings the original dataset occupies 974.43 MB in a plain text file with four columns: object identifier, time instant, coordinate x and coordinate y. Every value of these columns are stored as a string. However, to obtain a more precise compression measure, we represent this information in a binary file using two bytes to represent object identifiers (max value 3,653), two bytes for the instant column (max value 44,641), two bytes for the x-axis (max value 2,723) and three bytes for the y-axis (max value 367,775). Therefore, the binary representation of our dataset occupies 395.07 MB.