## Welcome!

This website gives a brief overview on my research, teaching, and professional background with further references.

I am conducting research in mathematical programming and operations research, on the edge between computer science, mathematics, and economics. While there is undoubtably a focus on computational methods and numerical implementations of high performance, theoretical investigations and analyses are a steady part of my scientific work. More specifically, my research interests include (but are not limited to):

- Mathematical Programming & Operations Research
- Discrete Algorithms & Combinatorial Optimization
- (Mixed-)Integer Linear Programming, Binary Quadratic Programming
- Linear, (Convex) Quadratic, and Semidefinite Programming
- Branch-&-Cut Algorithms, Reformulation and Linearization Techniques
- Graph Theory, Polyhedral Theory, Algorithmic Game Theory
- Combinatorial Algorithms & Data Structures
- Algorithm Engineering and High Performance Computing
- Graph Algorithms and Graph Drawing
- Data and Network Analysis

Typically, the emphasis of my theoretical and computational work is on a better solution of optimization or decision making problems in practice. This may be, e.g., by improving or reformulating models, by sophisticated computational advances such as engineered separation algorithms, by exploiting structures to derive tailored preprocessing, linearization, or solution methods, or by enhancing generic solution methods themselves.

Please find below a selection of current research projects, and listings of publications.

The above mentioned scientific fields are also an integral part of my
**teaching** while my experience and
portfolio covers also several further areas in Mathematics, Computer Science,
and Economics.

## Academic Background & Professional Appointments

Since April 2024, I am an interim full professor for Management Science at the University of Siegen, Germany.

Moreover, since April 2020, I am affiliated with the
High Performance Computing & Analytics Lab
of the
University of Bonn, Germany.

My prior academic background is as follows:

- 10/2019-03/2020: Research Associate (Postdoc) - Dept. of Mathematics & Computer Science - University of Cologne
- 04/2019-09/2019: Interim (Full) Professor for Discrete Optimization - Dept. of Mathematics & Computer Science - University of Cologne
- 01/2015-03/2019: Research Associate (Postdoc) - Dept. of Mathematics & Computer Science - University of Cologne
- 01/2015: PhD in Computer Science - University of Cologne
- 04/2009-01/2015: Research Assistant (PhD Candidate) - Dept. of Mathematics & Computer Science - University of Cologne
- 11/2008: Diploma in Computer Science - Technical University of Dortmund. Germany

## Research Projects

This a collection of selected research directions and projects with recent developments and publications.

#### Maximum Cut Problem (MaxCut) and Quadratic Unconstrained Binary Optimization (QUBO)

I work on exact methods for these two strongly related problems from various perspectives.

- Integration and common enhancement of solution techniques from Polyhedral Combinatorics, Integer Linear Programming, and Semidefinite Programming in a collaboration with Angelika Wiegele.
- For MaxCut, I combine classic theory and novel insights to obtain
*Integer Programming Formulations based on Spanning Trees*. The corresponding paper is accepted for ISCO 2024, and a preprint is here. - Techniques for the separation of
*facet-defining*odd-cycle inequalities, giving a leap to exact solvers: One and Two - Exact solvers for sparse instances based on Integer Programming, like McSparse
- The Spin Glass Server
- A new instance library with meta data information, see a prototype
**here**

#### Methods for Constrained Binary Quadratic Optimization

- I develop the
theory
and work on the
computational effectiveness
of the
**Inductive Linearization Technique**for binary programs with linear constraints and either a quadratic objective function, or quadratic constraints, or both. Effectively, it generates a (often small) subset of the constraints defining a first-level RLT of the original program whose addition - by construction - suffices to linearize it without any further effort. - Further, I worked out an inexact simplex algorithm that performs quadratic optimization over the vertices of (0-1) polyhedra.

#### Sophisticated Mixed-Integer Programming and Algorithms for Combinatorial Optimization

It is my passion to design and improve mathematical models with emphasis on their
better practical solution. Moreover, I develop sophisticated solution techniques
like Branch-and-Cut Algorithms that go far beyond “plugging a model into a solver”.
In this line of research, I have tackled various optimization problems with many
interdisciplinary applications, and gained particularly an expert for *ordering
and assignment (matching) problems*. The most recent publications deal with:

- Asymmetric Betweenness / Quadratic Linear Ordering Problems with some relations to Facility Layout
- Treewidth

## Publications

A full publication
list (i.e., with theses, recent articles to appear, as well as preprints)
is here.

A list of peer-reviewed publications is available via
ORCID.

Finally, you might also take a look at
DBLP, however,
as you see some of the rather math-oriented journal publications are either not
listed there or only listed with a quite large delay.