The graph edit distance (GED) quantifies the dissimilarity of two graphs as the minimum cost of a sequence of edit operations turning one graph into the other. The problem complexity depends on the choice of the edit operation costs and the properties of the considered graphs. It has been shown that the classical NP-hard subgraph isomorphism problem (SI) and the maximum common subgraph problem (MCS) can be reduced to computing the GED. As a consequence, computing the GED also is NP-hard. However, for SI and MCS a fine distinction of the complexity depending on parameters such as treewidth, degree, and their combination is known. The goal of this project is to investigate the complexity of computing the graph edit distance in restricted graph classes identifying polynomial-time solvable and NP-hard cases.

Requirements: Strong interest in graph algorithms and theoretical computer science

Contact: Nils Kriege