On the Relevance of Local Neighbourhoods for Greedy Graph Edit Distance

Approximation of graph edit distance based on bipartite graph matching emerged to an important model for distance based graph classification. However, one of the drawbacks of this particular approximation is its cubic runtime with respect to the number of nodes of the graphs. In fact, this runtime restricts the applicability of bipartite graph matching to graphs of rather small size. Recently, a new approximation for graph edit distance using greedy algorithms (rather than optimal bipartite algorithms) has been proposed. This novel algorithm reduces the computational complexity to quadratic order. In another line of research it has been shown that the definition of local neighbourhoods plays a crucial role in bipartite graph matching. These neighbourhoods define the local substructures of the graphs which are eventually assigned to each other. In the present paper we demonstrate that the type of local neighbourhood and in particular the distance model defined on them is also highly relevant for graph classification using greedy graph edit distance.