Abstract
The number and size of RDF knowledge graphs grows continuously. Efficient storage solutions for these graphs are indispensable for their use in real applications. We present such a storage solution dubbed Tentris. Our solution represents RDF knowledge graphs as sparse order-3 tensors using a novel data structure, which we dub hypertrie. It then uses tensor algebra to carry out SPARQL queries by mapping SPARQL operations to Einstein summation. By being able to compute Einstein summations efficiently, Tentris outperforms the commercial and open-source RDF storage solutions evaluated in our experiments by at least 1.8 times with respect to the average number of queries it can serve per second on three datasets of up to 1 billion triples. Our code, evaluation setup, results, supplementary material and the datasets are provided at https://tentris.dice-research.org/iswc2020.
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Notes
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- 3.
Note that indexes for different collation orders are crucial for the performance of triple stores. They determine which join orders are possible and which triple patterns are cheap to resolve. However, building indexes comes at a cost: each index takes additional time to build and update. It also requires additional memory. Consequently, there is always a trade-off between querying speed on the one hand and memory consumption and maintenance cost on the other hand.
- 4.
Tensors can be defined in a more general manner than provided herein, see [2] for details.
- 5.
Technically, SPARQL semantics define solution mappings as partial functions f. Our formal model is equivalent and simply maps all variables for which f is not defined to \(\epsilon \).
- 6.
It may not be defined if t contains any resource that is not in \(\mathinner {\mathrm {dom}}(id)\).
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The full setup is available as Ansible playbook at https://github.com/dice-group/tentris-paper-benchmarks/releases/tag/v1.0.
- 8.
We used this version because of query logs being available for FEASIBLE.
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For each template one query was generated. Additionally, queries not projecting all variables were included with and without DISTINCT.
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Virtuoso has a limit of \(2^{20}\) results for queries answered via HTTP (see issue https://github.com/openlink/virtuoso-opensource/issues/700).
- 11.
All queries can be found in the supplementary material.
- 12.
We extended TripleBit to support entering SPARQL queries via command-line interface directly. This modification was necessary to use TripleBit with IGUANA. Code available at: https://github.com/dice-group/TripleBit/releases/tag/2020-03-03.
- 13.
As IGUANA requires SPARQL Protocol conformance, we fixed the HTTP request handling of gStore, i.e., parsing requests, naming of parameters, and response content-type. With respect to benchmark execution, we set the timeout to 3 min, and the thread limit to 32 and raised the total memory limit to \(800\)GB. Code available at: https://github.com/dice-group/gStore-1/releases/tag/3b4fe58-mod.
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Acknowledgments
The authors would like to thank Lennart Austenfeld for automating the evaluation setup. This work has been supported by the German Federal Ministry for Economic Affairs and Energy (BMWi) within the project RAKI under the grant no 01MD19012D, by the German Federal Ministry of Education and Research (BMBF) within the project DAIKIRI under the grant no 01IS19085B, and by the EU H2020 Marie Skłodowska-Curie project KnowGraphs under the grant agreement no 860801.
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Bigerl, A., Conrads, F., Behning, C., Sherif, M.A., Saleem, M., Ngonga Ngomo, AC. (2020). Tentris – A Tensor-Based Triple Store. In: Pan, J.Z., et al. The Semantic Web – ISWC 2020. ISWC 2020. Lecture Notes in Computer Science(), vol 12506. Springer, Cham. https://doi.org/10.1007/978-3-030-62419-4_4
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