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Discrete or combinatorial optimization is a branch of mathematics, in particular discrete mathematics. It is concerned with solving discrete, finite optimization problems efficiently.

The methods and results of modern discrete optimization touch different areas of discrete mathematics and computer science, for example, combinatorics, graph theory, discrete probability theory, finite harmonic analysis, design, analysis and the theory of complexity.

A central topic in discrete optimization is the design of efficient algorithms for NP-hard discrete optimization problems using sub-optimal paradigms such as randomization or approximation. Specific research topics of the group are:

  • randomized and de-randomized algorithms, e.g. set and vertex cover, hypergraph matching, verticle routing
  • algorithms for big data problems, e.g. graph matching, path and Euler paths
  • Other focus areas are:
  • combinatorial and geometric discrepancy theory (hypergraphs with arithmetic structures)
  • combinatorial game theory (Mastermind, Maker-Braker Games).

The group is involved in interdisciplinary research projects within the cluster of excellence „The Future Ocean“ and further projects in medicine and life sciences. A special attention is given to the international cooperation with Indian universities, among them the Dayalbagh Educational Institute, Deemed University, Agra and the Indian Institutes of Technology in Delhi, Kanpur and Bombay.

The group is or was part of several high competitive research clusters. Among them are the cluster of excellence „The Future Ocean“, the DFG priority programme 1736 „Algorithms for Big Data“ and the DFG priority programme 1307 „Algorithm Engineering“ (2007- 2016) and the DFG SPP 1126 „Large and Complex Networks“ (2000-2007).

In Kiel the group is actively participating in the (AU research foci Kiel Marine Science (KMS) and Kiel Life Science (KLS).

A. Srivastav is PI in the cluster of excellence „The Future Ocean“ and co-speaker of the Research Platforms of „The Future Ocean“. He served as a member of the executive boards of „The Future Ocean“ from 2008-2019. In the research focus Kiel Marine Science A. Srivastav is co-speaker of the focus area Digital Ocean. He is also speaker of the council for scientific computing and digital reseach infrastructures at Kiel University.