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.