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Applicability of SQL/SPARQL Query Optimizations to Tensor Algebra

Master Thesis

Task

Today, tensors are used in many computationally demanding areas, such as machine learning in deep learning, quantum physics and chemistry, or in the tensor-based triplestore (Tentris) developed by the Data Science working group. Sparsely occupied tensors play a special role, i.e. those for which most entries are zero.

In this work, the student first obtains an overview of well-established methods for query optimization in SQL and SPARQL and then analyses the applicability to a (simplified) tensor algebra.

(Master) Promising optimization approaches are also to be implemented and evaluated for Tentris.

In short: What is a tensor?

Well, a simple number, also called a scalar, is a 0-dimensional object. A vector is obviously 1 dimensional and a matrix has 2 dimensions. If you now imagine a matrix that has a depth like a cube, then you have a "tensor of rank 3" or with three dimensions. Tensors can therefore be seen as a generalization of vectors and matrices with any number of dimensions.