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Publication# Efficient Streaming Subgraph Isomorphism with Graph Neural Networks

Abstract

Queries to detect isomorphic subgraphs are important in graph-based data management. While the problem of subgraph isomorphism search has received considerable attention for the static setting of a single query, or a batch thereof, existing approaches do not scale to a dynamic setting of a continuous stream of queries. In this paper, we address the scalability challenges induced by a stream of subgraph isomorphism queries by caching and re-use of previous results. We first present a novel subgraph index based on graph embeddings that serves as the foundation for efficient stream processing. It enables not only effective caching and re-use of results, but also speeds-up traditional algorithms for subgraph isomorphism in case of cache misses. Moreover, we propose cache management policies that incorporate notions of reusability of query results. Experiments using real-world datasets demonstrate the effectiveness of our approach in handling isomorphic subgraph search for streams of queries.

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Related concepts (33)

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Ontological neighbourhood

Graph isomorphism

In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H such that any two vertices u and v of G are adjacent in G if and only if and are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism being a structure-preserving bijection. If an isomorphism exists between two graphs, then the graphs are called isomorphic and denoted as . In the case when the bijection is a mapping of a graph onto itself, i.

Subgraph isomorphism problem

In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a subgraph that is isomorphic to H. Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. However certain other cases of subgraph isomorphism may be solved in polynomial time.

Graph isomorphism problem

The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. The problem is not known to be solvable in polynomial time nor to be NP-complete, and therefore may be in the computational complexity class NP-intermediate. It is known that the graph isomorphism problem is in the low hierarchy of class NP, which implies that it is not NP-complete unless the polynomial time hierarchy collapses to its second level.

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