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

TL;DR

EmbAssi introduces novel embedding-based lower bounds for graph edit distance, enabling efficient similarity search in large graph databases by reducing computational costs through effective filtering.

Contribution

The paper presents a new approach to embed assignment costs into $ ext{l}_1$ space using tree metrics, significantly improving filtering efficiency for large graph databases.

Findings

Lower bounds are close to exact graph edit distances in real-world graphs.

Index construction and search scale to databases with millions of graphs.

Embedding costs into $ ext{l}_1$ space enables fast filtering in large datasets.

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 efficiently for large databases with up to millions of graphs. We build on the filter-verification paradigm, where lower and upper bounds are used to reduce the number of exact computations of the graph edit distance. Highly effective 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 verification. In this work, we derive novel lower bounds for efficient filtering from restricted assignment problems, where the cost function is a tree metric. This special case allows embedding the costs of optimal assignments isometrically into $\ell_1$ space, rendering efficient indexing possible. We propose several lower bounds of the graph edit distance obtained from tree metrics reflecting the edit costs, which are combined for effective filtering. Our method termed EmbAssi can be integrated into existing filter-verification pipelines as a fast and effective pre-filtering step. Empirically we show that for many real-world graphs our lower bounds are already close to the exact graph edit distance, while our index construction and search scales to very large databases.