Metric Indexing for Graph Similarity Search

TL;DR

This paper introduces a new metric indexing framework for graph similarity search that efficiently handles graphs with arbitrary attributes and non-uniform edit costs, significantly improving search speed.

Contribution

It presents a filter-verification framework supporting non-uniform edit costs and arbitrary attributes, extending existing methods beyond categorical labels and uniform costs.

Findings

Achieves significant runtime improvements over linear scan.

Outperforms state-of-the-art methods in experiments.

Supports graphs with arbitrary attributes and non-uniform costs.

Abstract

Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and naturally supports graphs with vertex and edge attributes. Since its computation is NP-hard, techniques for accelerating similarity search have been studied extensively. However, index-based approaches for this are almost exclusively designed for graphs with categorical vertex and edge labels and uniform edit costs. We propose a filter-verification framework for similarity search, which supports non-uniform edit costs for graphs with arbitrary attributes. We employ an expensive lower bound obtained by solving an optimal assignment problem. This filter distance satisfies the triangle inequality, making it suitable for acceleration by metric indexing. In subsequent stages, assignment-based upper bounds are used to avoid further exact distance computations. Our extensive experimental evaluation shows that a significant runtime advantage over both a linear scan and state-of-the-art methods is achieved.