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Similarity search is the problem of finding in a collection of objects those that are similar to a given query object. It is a fundamental problem in modern applications and the objects considered may be as diverse as locations in space, text documents, images, twitter messages, or trajectories of moving objects. In this paper we are motivated by the latter application. Trajectories are recorded movements of mobile objects such as vehicles, animals, public transportation, or parts of the human body. We propose a novel distance function called DistanceAvg to capture the similarity of such movements. To be practical, it is necessary to provide indexing for this distance measure. Fortunately we do not need to start from scratch. A generic and unifying approach is metric space, which organizes the set of objects solely by a distance (similarity) function with certain natural properties. Our function DistanceAvg is a metric. Although metric indexes have been studied for decades and many such structures are available, they do not offer the best performance with trajectories. In this paper we propose a new design, which outperforms the best existing indexes for kNN queries and is equally good for range queries. It is especially suitable for expensive distance functions as they occur in trajectory similarity search. In many applications, kNN queries are more practical than range queries as it may be difficult to determine an appropriate search radius. Our index provides exact result sets for the given distance function., Comment: 54 pages, 26 figures

In today's world data is being generated at a high rate due to which it has become inevitable to analyze and quickly get results from this data. Most of the relational databases primarily support SQL querying with a limited support for complex data analysis. Due to this reason, data scientists have no other option, but to use a different system for complex data analysis. Due to this, data science frameworks are in huge demand. But to use such a framework, all the data needs to be loaded into it. This requires significant data movement across multiple systems, which can be expensive. We believe that it has become the need of the hour to come up with a single system which can perform both data analysis tasks and SQL querying. This will save the data scientists from the expensive data transfer operation across systems. In our work, we present DaskDB, a system built over the Python's Dask framework, which is a scalable data science system having support for both data analytics and in situ SQL query processing over heterogeneous data sources. DaskDB supports invoking any Python APIs as User-Defined Functions (UDF) over SQL queries. So, it can be easily integrated with most existing Python data science applications, without modifying the existing code. Since joining two relations is a very vital but expensive operation, so a novel distributed learned index is also introduced to improve the join performance. Our experimental evaluation demonstrates that DaskDB significantly outperforms existing systems.