Raphael Reitzig

Proportional apportionment is the problem of assigning seats to states (resp. parties) according to their relative share of the population (resp. votes), a field heavily influenced by the early work of Michel Balinski, not least his influential 1982 book with Peyton Young (Fair representation, 2nd edn. Brookings Institution Press, Washington, D.C.,...

Given a set of n sticks of various (not necessarily different) lengths, what is the largest length so that we can cut k equally long pieces of this length from the given set of sticks? We analyze the structure of this problem and show that it essentially reduces to a single call of a selection algorithm; we thus obtain an optimal linear-time algori...

Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms that implement divisor methods: one by Cheng and Eppstein (ISAAC, 2014) has worst-case optimal running time bu...

Segal-Halevi, Hassidim, and Aumann (AAMAS, 2015) propose the problem of cutting sticks so that at least k sticks have equal length and no other stick is longer. This allows for an envy-free allocation of sticks to k players, one each. The resulting number of sticks should also be minimal. We analyze the structure of this problem and devise a linear...

Recent results on Java 7's dual pivot Quicksort have revealed its highly asymmetric nature. These insights suggest that asymmetric pivot choices are preferable to symmetric ones for this Quicksort variant. From a theoretical point of view, this should allow us to improve on the current implementation in Oracle's Java 7 runtime library. In this pape...

Recent results on Java 7's dual pivot Quicksort have revealed its highly asymmetric nature. These insights suggest that asymmetric pivot choices are preferable to symmetric ones for this Quicksort variant. From a theoretical point of view, this should allow us to improve on the current implementation in Oracle's Java 7 runtime library. In this pape...

This thesis discusses whether and how dynamic programming recursions can be computed in parallel such that compilers can parallelise them automatically. We discover that under certain assumptions which permit a rich class of dynamic programming recursions, two kinds of recursions can be computed in parallel while others can not. For those which can...

The study of microbial diversity and community structures heavily relies on the analyses of sequence data, predominantly taxonomic marker genes like the small subunit of the ribosomal RNA (SSU rRNA) amplified from environmental samples. Until recently, the "gold standard" for this strategy was the cloning and Sanger sequencing of amplified target g...

Dowell and Eddy (2004) presented several context free grammars for RNA secondary structure prediction. Some of them are claimed to be unambiguous with respect to secondary structures. Although this property is crucial for the correctness of prediction algorithms using those grammars, it is only shown empirically, but not formally proven. This gap i...

Considering computer or real world systems with sensitive data, it is obvious that the issue of system security is very important for our society. Thus, verifying the security of a system is a problem we want to solve. However, to attack this problem at all we rst need proper representations of systems that allow the formulation of properties regar...