44 lines
3.9 KiB
Markdown
44 lines
3.9 KiB
Markdown
## Chase Algorithm Resources
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### Papers
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| Paper | Authors | Link |
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|:--------------------------------------------|:-------------------------|:-------------------------------------------------------------------------------------|
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| The Theory of Joins in Relational Databases | Aho, Beeri & Ullman | [dl.acm.org/doi/10.1145/320083.320091](https://dl.acm.org/doi/10.1145/320083.320091) |
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| Testing Implications of Data Dependencies | Maier, Mendelzon & Sagiv | [dl.acm.org/doi/10.1145/320107.320115](https://dl.acm.org/doi/10.1145/320107.320115) |
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### Algorithm Variants
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| Variant | Output Size | Speed per Step | Satisfaction Check | Used By | Best For |
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|:---------------|:------------|:---------------|:-------------------|:------------------|:----------------------------------------------|
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| Oblivious | Largest | Fastest | None | — | Prototyping; when output size doesn't matter |
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| Skolem | Medium | Fast | Implicit (Skolem terms) | VLog, Graal | Parallelism; data exchange; deterministic runs |
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| Restricted | Smallest | Slower | Explicit (homomorphism check) | RDFox, VLog | Production use; query performance over large KGs |
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| Core | Most compact | Slowest | Full core computation | — (theoretical) | Theoretical analysis; minimum representations |
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#### Variant Notes
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**Oblivious Chase** fires every applicable rule without checking whether the conclusion already holds. Simple to implement but produces redundant facts and is the hardest to guarantee termination for.
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**Skolem Chase** uses deterministic Skolem functions to generate nulls — the same rule trigger always produces the same null. This makes it idempotent and easy to parallelize, with no need to track which rules have already fired.
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**Restricted Chase** checks before firing whether the rule head is already satisfied via a homomorphism into the current database. Never adds redundant facts, producing the smallest universal solution. The homomorphism check is NP-hard in general but fast in practice with good indexing.
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**Core Chase** goes further than the restricted chase, computing the logical core — the most compressed possible universal solution. Theoretically important but computationally expensive; not used in production engines.
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### Chase Query Engines
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| Engine | Organization | Chase Variant | Home Page |
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|:---------|:-------------------------------|:-------------------|:-------------------------------------------------------------------------------------|
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| RDFox | Oxford Semantic Technologies | Restricted | [oxfordsemantic.tech/rdfox](https://oxfordsemantic.tech/rdfox) |
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| VLog | TU Dresden / VU Amsterdam | Restricted + Skolem | [github.com/karmaresearch/vlog](https://github.com/karmaresearch/vlog) |
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| Graal | LIRMM, Montpellier | Skolem + Oblivious | [graphik-team.github.io/graal](https://graphik-team.github.io/graal) |
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| Vadalog | University of Oxford / TU Wien | Warded (Restricted variant) | [vadalog-system.com](https://vadalog-system.com) |
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| PDQ | University of Oxford | Skolem | [github.com/michaelbenedict/pdq](https://github.com/michaelbenedict/pdq) |
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| Llunatic | University of Genova | Skolem | [github.com/donatellosantoro/Llunatic](https://github.com/donatellosantoro/Llunatic) |
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## Changelog
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* **Mar 6, 2026** -- Added algorithm variants section; added chase variant column to engines table.
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* **Mar 5, 2026** -- Re-formatted the table for the papers section.
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* **Mar 5, 2026** -- The first version was created. |