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Next generation algorithms for grabbing and exploiting symmetry

Project description

Boosting the search for symmetry

Detecting symmetry in large and complex data systems is increasingly important in computing. Whether you’re looking at mathematical equations, graphs, road maps or the way social networks evolve, certain repeating patterns occur which can be identified and used to make computation more efficient. Importantly, symmetry detection can help avoid duplication and identify patterns in very complex systems such as neural networks used in machine learning, or in large databases, such as those listing chemical molecules. Developing efficient algorithms for symmetry detection is also known as the Graph Isomorphism Problem - one of the biggest open problems in theoretical computer science. The EU-funded EngageS project will develop theoretical models and software tools to efficiently detect symmetry.

Objective

Symmetry is a phenomenon that appears in many different contexts.
Algorithmic symmetry detection and exploitation is the concept of finding intrinsic symmetries of a given object and then using these symmetries to our advantage. Application areas of algorithmic symmetry detection and exploitation range from convolutional neural networks in machine learning to computer graphics, chemical data bases and beyond.
In contrast to this widespread use, our understanding of the theoretical foundation (namely the graph isomorphism problem) is incomplete and current algorithmic symmetry tools are inadequate for big data applications. Hence, EngageS addresses these key challenges in the field using a systematic approach to the theory and practice of symmetry detection. It thereby also fixes the existing lack of interplay between theory and practice, which is part of the problem.

EngageS' main aims are to tackle the classical and descriptive complexity of the graph isomorphism problem and to design the next generation of symmetry detection algorithms. As key ideas to resolve the complexity, EngageS offers three new approaches on how to prove lower bounds and a new method to settle the descriptive complexity.

EngageS will also develop practical symmetry detection algorithms for big data, exploiting parallelism and memory hierarchies of modern machines, and will introduce the concept of and a road map to exploiting absence of symmetry. Overall EngageS will establish a comprehensive software library that will serve as a platform for integrated research on the algorithmic treatment of symmetry.

In summary, EngageS will develop fast, efficient and accessible symmetry detection tools that will be used to solve complex algorithmic problems in a range of fields including combinatorial algorithms, generation problems, and canonization.

Host institution

TECHNISCHE UNIVERSITAT DARMSTADT
Net EU contribution
€ 1 645 758,66
Address
KAROLINENPLATZ 5
64289 Darmstadt
Germany

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Region
Hessen Darmstadt Darmstadt, Kreisfreie Stadt
Activity type
Higher or Secondary Education Establishments
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Total cost
€ 1 645 758,66

Beneficiaries (2)