Capturing Topology in Graph Pattern Matching (1201.0229v1)

Abstract: Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be conducted in cubic-time. However, they fall short of capturing the topology of data graphs, i.e., graphs may have a structure drastically different from pattern graphs they match, and the matches found are often too large to understand and analyze. To rectify these problems, this paper proposes a notion of strong simulation, a revision of graph simulation, for graph pattern matching. (1) We identify a set of criteria for preserving the topology of graphs matched. We show that strong simulation preserves the topology of data graphs and finds a bounded number of matches. (2) We show that strong simulation retains the same complexity as earlier extensions of simulation, by providing a cubic-time algorithm for computing strong simulation. (3) We present the locality property of strong simulation, which allows us to effectively conduct pattern matching on distributed graphs. (4) We experimentally verify the effectiveness and efficiency of these algorithms, using real-life data and synthetic data.

Capturing Topology in Graph Pattern Matching

The paper "Capturing Topology in Graph Pattern Matching" addresses a prevalent challenge in graph pattern matching by introducing a novel concept termed "strong simulation." Traditional approaches to graph pattern matching primarily rely on subgraph isomorphism, an NP-complete problem, which proves infeasible for large-scale data due to its high computational complexity. To mitigate this issue, the authors explore graph simulation techniques that allow cubic-time matching, though these often fail to preserve the necessary topological nuances within data graphs. This paper proposes strong simulation as a robust alternative that captures topology effectively while maintaining the computational efficiency of early graph simulation extensions.

The principal contributions of the paper are multifaceted:

1. Topology Preservation Criteria: Strong simulation is rigorously defined using topology preservation criteria, ensuring both child and parent relationships in node mappings. Unlike standard simulation techniques, strong simulation maintains connectivity and cyclic relationships in the matched subgraphs, providing a better semantic fit between pattern graphs and data graphs.
2. Complexity Considerations and Algorithm Development: The authors present a cubic-time algorithm to compute strong simulation efficiently. They demonstrate that strong simulation, despite its enhanced topological preservation, retains the same complexity level as other simulation-based methods. Additionally, optimization techniques are introduced to minimize query execution time, including dual simulation filtering, query minimization, and connectivity pruning.
3. Locality Property for Distributed Processing: A key innovation in strong simulation is its locality property, which enables effective pattern matching in distributed graph environments. This property reduces unnecessary data shipment across network nodes and allows partial computations to be consolidated into comprehensive results.
4. Experimental Validation: Extensive experimental studies with real-life (Amazon, YouTube) and synthetic datasets validate the efficacy and scalability of strong simulation. The research verifies that strong simulation identifies sensible matches that subgraph isomorphism often misses, and it avoids the excessive matches generated by conventional simulation techniques. Performance metrics indicate substantial improvements in match quality and execution efficiency, particularly with Match+ optimizations yielding time reductions by approximately one-third.

The implications of this research are significant for applications in social networks, biology, and intelligence analysis, where preserving the topology of graph data is critical. Strong simulation presents a promising model that balances the intricate demands of topological fidelity with computational feasibility. Its ability to seamlessly integrate into distributed processing environments further demonstrates its utility in handling large-scale graph data, paving the way for future advancements in AI-related graph analytics.

In speculating on future developments, extending strong simulation to accommodate more sophisticated edge constraints, such as regular expressions, could enhance its expressiveness and applicability across diverse datasets. Continued exploration into distributed algorithms and ranking metrics for match results will optimize query performance and prioritization, beneficial for real-time analytics and decision-making processes. The paper clearly establishes strong simulation as a pivotal stride towards overcoming the limitations of subgraph isomorphism, contributing to the foundation for more advanced graph pattern matching methodologies.