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.
ScdcCT was implemented as a classical compressed baseline to compare against GraCT @cite_9 . It uses the same components, snapshots and logs, but the logs are compressed with differences and not with grammars. The differences are compressed using @math -Dense Codes @cite_2 , a fast-to-decode variable-length code that has low redundancy over the zero-order empirical entropy of the sequence. This exploits the fact that short movements to contiguous cells are more frequent than movements to distant cells.
@cite_9 @cite_2
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Much research has been published about trajectory management on the ground or at the sea, but compression or indexing of flight trajectories have usually been less explored. However, air traffic management is a challenge because airspace is becoming more and more congested, and large flight data collections must be preserved and exploited for varied purposes. This paper proposes 3DGraCT, a new method for representing these flight trajectories. It extends the GraCT compact data structure to cope with a third dimension (altitude), while retaining its space time complexities. 3DGraCT improves space requirements of traditional spatio-temporal data structures by two orders of magnitude, being competitive for the considered types of queries, even leading the comparison for a particular one. Variants of Huffman codes where words are taken as the source symbols are currently the most attractive choices to compress natural language text databases. In particular, Tagged Huffman Code by offers fast direct searching on the compressed text and random access capabilities, in exchange for producing around 11 larger compressed files. This work describes End-Tagged Dense Code and (s, c)-Dense Code, two new semistatic statistical methods for compressing natural language texts. These techniques permit simpler and faster encoding and obtain better compression ratios than Tagged Huffman Code, while maintaining its fast direct search and random access capabilities. We show that Dense Codes improve Tagged Huffman Code compression ratio by about 10 , reaching only 0.6 overhead over the optimal Huffman compression ratio. Being simpler, Dense Codes are generated 45 to 60 faster than Huffman codes. This makes Dense Codes a very attractive alternative to Huffman code variants for various reasons: they are simpler to program, faster to build, of almost optimal size, and as fast and easy to search as the best Huffman variants, which are not so close to the optimal size.