EmbAssi: Embedding Assignment Costs for Similarity Search in Large Graph Databases

Abstract

The graph edit distance is an intuitive measure to quantify the dissimilarity of graphs, but its computation is NP-hard and challenging in practice. We introduce methods for answering nearest neighbor and range queries regarding this distance e ciently for large databases with up to millions of graphs. We build on the lter-veri cation paradigm, where lower and upper bounds are used to reduce the number of exact computations of the graph edit distance. Highly e ective bounds for this involve solving a linear assignment problem for each graph in the database, which is prohibitive in massive datasets. Index-based approaches typically provide only weak bounds leading to high computational costs veri cation. In this work, we derive novel lower bounds for e cient ltering from restricted assignment problems, where the cost function is a tree metric. This special case allows embedding the costs of optimal assignments isometrically into ℓ 1 space, rendering e cient indexing possible. We propose several lower bounds of the graph edit distance obtained from tree metrics re ecting the edit costs, which are combined for e ective ltering. Our method termed EmbAssi can be integrated into existing lter-veri cation pipelines as a fast and e ective pre-ltering step. Empirically we show that for many realworld graphs our lower bounds are already close to the exact graph edit distance, while our index construction and search scales to very large databases.