Accelerating Graph Similarity Search through Integer Linear Programming

TL;DR

This paper introduces an efficient integer linear programming-based lower bound to accelerate graph similarity search under Graph Edit Distance constraints, significantly improving filtering performance in large graph databases.

Contribution

It proposes a novel hierarchy of lower bounds and an ILP formulation that enhances the filtering step in graph similarity search, outperforming existing methods.

Findings

Outperforms state-of-the-art algorithms on most thresholds

Efficient ILP-based lower bound dominates previous bounds

Significantly reduces computational time in graph similarity search

Abstract

The Graph Edit Distance (GED) is an important metric for measuring the similarity between two (labeled) graphs. It is defined as the minimum cost required to convert one graph into another through a series of (elementary) edit operations. Its effectiveness in assessing the similarity of large graphs is limited by the complexity of its exact calculation, which is NP-hard theoretically and computationally challenging in practice. The latter can be mitigated by switching to the Graph Similarity Search under GED constraints, which determines whether the edit distance between two graphs is below a given threshold. A popular framework for solving Graph Similarity Search under GED constraints in a graph database for a query graph is the filter-and-verification framework. Filtering discards unpromising graphs, while the verification step certifies the similarity between the filtered graphs and the query graph. To improve the filtering step, we define a lower bound based on an integer linear programming formulation. We prove that this lower bound dominates the effective branch match-based lower bound and can also be computed efficiently. Consequently, we propose a graph similarity search algorithm that uses a hierarchy of lower bound algorithms and solves a novel integer programming formulation that exploits the threshold parameter. An extensive computational experience on a well-assessed test bed shows that our approach significantly outperforms the state-of-the-art algorithm on most of the examined thresholds.