Upper Bounding the Graph Edit Distance Based on Rings and Machine Learning

TL;DR

This paper introduces a new framework and heuristics for upper bounding graph edit distance using rings and machine learning, significantly improving accuracy on topology-centric graph datasets.

Contribution

It unifies GED to LSAPE transformations, introduces rings as a novel local structure, and proposes two heuristics, RING and RING-ML, enhancing upper bound accuracy.

Findings

RING heuristic improves upper bounds on topology-rich datasets.

RING-ML leverages machine learning for better GED approximations.

Significant gap closure between fast heuristics and slow exact algorithms.

Abstract

The graph edit distance (GED) is a flexible distance measure which is widely used for inexact graph matching. Since its exact computation is NP-hard, heuristics are used in practice. A popular approach is to obtain upper bounds for GED via transformations to the linear sum assignment problem with error-correction (LSAPE). Typically, local structures and distances between them are employed for carrying out this transformation, but recently also machine learning techniques have been used. In this paper, we formally define a unifying framework LSAPE-GED for transformations from GED to LSAPE. We also introduce rings, a new kind of local structures designed for graphs where most information resides in the topology rather than in the node labels. Furthermore, we propose two new ring based heuristics RING and RING-ML, which instantiate LSAPE-GED using the traditional and the machine learning based approach for transforming GED to LSAPE, respectively. Extensive experiments show that using rings for upper bounding GED significantly improves the state of the art on datasets where most information resides in the graphs' topologies. This closes the gap between fast but rather inaccurate LSAPE based heuristics and more accurate but significantly slower GED algorithms based on local search.