Our group is involved in several national and international research projects, funded by the German Research Foundation (DFG), the European Commission (EU), and the Australian Research Council (ARC). For a list of finished research projects, see here.
The Hyperbolic Geometry of Networks
Network science is driven by the question which properties large real-world networks have and how we can exploit them algorithmically. Hyperbolic geometry has proven to be a useful tool in this regard. Our goal is to better understand the relationship between large real-world networks and hyperbolic geometry. We want to study properties of hyperbolic random graphs as well as embeddings of real-world networks into hyperbolic space. Moreover, we want to exploit these structural insights by developing algorithms that perform provably well on hyperbolic random graphs and, in turn, empirically well on real-world networks.
Principal Investigator:Tobias Friedrich Participating Investigator:Thomas Bläsius Project term: Granted Februar 2018 Funded by: German Research Foundation (DFG)
All medium and large corporations are required to have their financial statements reviewed by an auditor. Each auditor has a certain set of skills and available time slots. Performing an audit requires different skills at different times. This results in a complex scenario with many hard and soft constraints to satisfy. In corporation with KPMG AG Wirtschaftsprüfungsgesellschaft, eight bachelor and three PhD students work on a new scheduling algorithm.
This project brings together theoreticians and practitioners who are working in the field of nature-inspired search and optimization heuristics. Its goal is on one hand to make theoretical findings more accessible for researchers and engineers who are concerned with applications, on the other hand to make theoreticians aware of practical problems and the kind of questions that arise in practical applications.
Bio-inspired Computing for Problems with Dynamically Changing Constraints
The aim of this project is to design bio-inspired computing methods for dynamically changing environments. Dynamic problems arise frequently in the areas of engineering, logistics, and manufacturing. Such problems are usually subject to a large set of constraints that change over time due to changes in resources. Algorithms that can deal with such dynamic changes would benefit decision-makers. The project aims to provide a foundational theory as the basis for the design of bio-inspired algorithms dealing with dynamically changing constraints and provide approaches for dealing with important industrial problems.
This project aims at using mathematical methods to identify the theoretical foundations of the capabilities and limits of computational learning. It uses a framework for learning criteria which allows for general statements, informing about many learning criteria at once.
Principal Investigator:Timo Kötzing Project term: Granted September 2015 Funded by: German Research Foundation (DFG)
Bio-inspired swarm algorithms are well established in practice for solving optimization problems with complex constraints even in difficult domains involving uncertainty. This project analyzes theoretically swarm-based search heuristics for dynamically changing and stochastic objectives.
Despite a large body of theoretical studies on load balancing, most results do not match the complex and heterogenous structure of the underlying network and the corresponding load balancing tasks. This project bridges the gap between the well-studied homogenous setting and the theoretically much less understood heterogenous load balancing problems that occur in practice.
Principal Investigator:Tobias Friedrich Participating Investigator:Thomas Sauerwald Project term: Started October 2015 Funded by: German Research Foundation (DFG)
Completed Research Projects
The rest of this page lists our finished research projects.
The Navigation Data Standard (NDS) is a new regularization for map data used, for example, in portable navigation devices. It restricts the data to be only accessible in blocks corresponding to the earth’s grid. Due to the limited memory of portable devices, it is not possible to store the entire map in memory at once. In corporation with TomTom, five students work on new algorithmic approaches for efficient routing algorithms that load as few blocks as possible.
Biological evolution has produced an extraordinary diversity of organisms. Evolutionary computation has found many innovative solutions to optimisation and design problems. Both fields have studied the speed of adaptation independently, and with orthogonal approaches. This project brings together an interdisciplinary consortium from both fields to synergise these complementary approaches and to create the foundation of a unified quantitative theory describing the speed of adaptation in both biological and artificial evolution.
Looking for a parking place in urban areas is often time consuming and stressful. Up-to-date navigation systems are barely capable of directing the driver to a good nearby parking lot. This is mostly due to missing data about available parking places on the roadside and little research on this topic. In corporation with TomTom five students work on new algorithmic approaches for efficient on-street parking.
This project establishes the field of parameterised analysis of bio-inspired computing. It rigorously analyses features of instances of combinatorial optimisation problems and their impact on the runtime behaviour of bio-inspired computing methods such as evolutionary algorithms and ant colony optimisation.
Chief Investigator:Frank Neumann Partner Investigator:Tobias Friedrich Project term: January 2014 till December 2016 Funded by: Australian Research Council (ARC)
This project aims to analyze the average-case behavior of some known parameterized algorithms, mainly motivated by the recent encouraging experimental studies of these algorithms. Most of these studies record, compared to the worst-case analysis, a much more promising performance on real-world data.
Principal Investigator:Tobias Friedrich Project term: December 2013 till August 2016 Funded by: German Research Foundation (DFG)
Smoothed Parameterized Complexity
Two main approaches have been considered in dealing with NP-hard problems in the last decade. One is parameterized complexity theory. The other one follows a probabilistic way of analyzing problems and algorithms. This project aims at developing the necessary tools and theories to combine parametrized and smoothed complexity.
Principal Investigator:Tobias Friedrich Project term: January 2014 till June 2015 Funded by: German-Israeli Foundation for Scientific Research and Development
Theoretical Foundations of Swarm Intelligence
Swarm based randomized search heuristics such as ant colony optimization (ACO) and particle swarm optimization (PSO) are established in various applications and particularly in dynamic optimization problems, providing good solutions. Unlike e.g. in evolutionary algorithms (EAs), hardly any theoretical foundations existed before the project started. The main purpose of this research project was to analyze the efficiency of different approaches.
Our research focus is on theoretical computer science and algorithm engineering. We are equally interested in the mathematical foundations of algorithms and developing efficient algorithms in practice. A special focus is on random structures and methods.