A graph isomorphism is a mapping between the nodes of two graphs that preserves the edges. An automorphism is an isomorphism of a graph to itself. The (non-trivial) automorphisms intuitively represent the symmetries of a graph. Two vertices are considered equivalent if there is an automorphism that maps one vertex to the other. The corresponding equivalence classes are referred to as orbit partition. The orbit partition is of interest for symmetry breaking techniques for various combinatorial problems. Identifying and pruning symmetric branches in the search tree based on the symmetries of the input instance can lead to drastic speed-ups. This project aims to develop dynamic algorithms for maintaining the orbit partition when the input graph changes. The focus of the project can be on the development and theoretical analysis of algorithms or their implementation and experimental evaluation.

Requirements: Strong interest in algorithms

Contact: Nils Kriege, Christian Schulz, Kathrin Hanauer