Fractional jumps: complete characterisation and an explicit infinite family

In this paper we provide a complete characterisation of transitive fractional jumps by showing that they can only arise from transitive projective automorphisms. Furthermore, we prove that such construction is feasible for arbitrarily large dimension by exhibiting an infinite class of projectively primitive polynomials whose companion matrix can be used to define a full orbit sequence over an affine space

Composite Key Generation on a Shared-Nothing Architecture

Generating synthetic data sets is integral to benchmarking, debugging, and simulating future scenarios. As data sets become larger, real data characteristics thereby become necessary for the success of new algorithms. Recently introduced software systems allow for synthetic data generation that is truly parallel. These systems use fast pseudorandom number generators and can handle complex schemas and uniqueness constraints on single attributes. Uniqueness is essential for forming keys, which identify single entries in a database instance. The uniqueness property is usually guaranteed by sampling from a uniform distribution and adjusting the sample size to the output size of the table such that there are no collisions. However, when it comes to real composite keys, where only the combination of the key attribute has the uniqueness property, a different strategy needs to be employed. In this paper, we present a novel approach on how to generate composite keys within a parallel data generation framework. We compute a joint probability distribution that incorporates the distributions of the key attributes and use the unique sequence positions of entries to address distinct values in the key domain