Graph pattern mining is important for analyzing graph data. Graph mining systems typically require answering pattern matching queries, which involve solving the NP-complete subgraph isomorphism problem. To address this, domain experts often develop custom pattern matching query optimization strategies based on exploiting substructural similarities across different patterns. While these optimizers can be effective, their development is challenging due to the complex structural properties of the patterns (e.g., subsymmetries), which are difficult to address. This complexity limits the exploration of interactions between different optimization strategies and restricts experts from continuously improving the optimizers—such as by incorporating additional custom or general pattern-based equivalences over time. In this paper, we present a programmable pattern matching query optimizer called Geo , which automatically manages the interactions between various equivalences, ensures the optimizations maintain correctness of results, and simplifies the management of substructure equivalences. Geo exposes a simple but flexible language for expressing pattern equivalences as rewrite rules. By maintaining canonical representations of generated patterns during equality saturation, Geo avoids issues arising from syntactic differences in isomorphic patterns. Additionally, we develop embedded reconstructablility ( EmRec ) that tracks provenance across equivalences to ensure various reconstructability needs of desired outputs. Our evaluation demonstrates that Geo can discover novel query equivalences through complex composition of various rewrite rules, enabling our optimized queries to achieve a cost reduction of up to 99% compared to the queries in prior work. We further test Geo ’s effectiveness at speeding up practical graph mining problems by using it in two representative case studies – approximate pattern matching and quasi-clique mining, and find it is highly effective at optimizing these tasks, enabling cost reductions of up to 71%.

While graph mining systems employ efficient task-parallel strategies to quickly explore subgraphs of interest (or matches), they remain oblivious to containment constraints like maximality and minimality, resulting in expensive constraint checking on every explored match as well as redundant explorations that limit their scalability.

We present a verification-based Byzantine Fault Tolerant processing system, called OsirisBFT, for distributed task-parallel applications. OsirisBFT treats computation tasks differently from state update tasks, allowing the application to scale independently from number of expected failures. OsirisBFT captures application-specific verification semantics via generic verification operators and employs lightweight verification strategies with little coordination during graceful execution. Evaluation across multiple applications and workloads shows that OsirisBFT delivers high processing throughput and scalability compared to replicated processing. Importantly, the scalable nature of OsirisBFT enables it to reduce the performance gap compared to baseline with no fault tolerance by simply scaling out.

Graph mining applications analyze the structural properties of large graphs. These applications are computationally expensive because finding structural patterns requires checking subgraph isomorphism, which is NP-complete. This paper exploits the sub-structural similarities across different patterns by employing Subgraph Morphing to accurately infer the results for a given set of patterns from the results of a completely different set of patterns that are less expensive to compute. To enable Subgraph Morphing in practice, we develop efficient query transformation techniques as well as automatic result conversion strategies for different application scenarios. We have implemented Subgraph Morphing in four state-of-the-art graph mining and subgraph matching systems: Peregrine, AutoMine/- GraphZero, GraphPi, and BigJoin; a thorough evaluation demonstrates that Subgraph Morphing improves the performance of these four systems by 34×, 10×, 18×, and 13×, respectively.

Graph mining workloads aim to extract structural properties of a graph by exploring its subgraph structures. General purpose graph mining systems provide a generic runtime to explore subgraph structures of interest with the help of user-defined functions that guide the overall exploration process. However, the state-of-the-art graph mining systems remain largely oblivious to the shape (or pattern) of the subgraphs that they mine. This causes them to: (a) explore unnecessary subgraphs; (b) perform expensive computations on the explored subgraphs; and, (c) hold intermediate partial subgraphs in memory; all of which affect their overall performance. Furthermore, their programming models are often tied to their underlying exploration strategies, which makes it difficult for domain users to express complex mining tasks.