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Article Dans Une Revue Journal of Artificial Intelligence Research Année : 2018

When Subgraph Isomorphism is Really Hard, and Why This Matters for Graph Databases

James Trimble
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Résumé

The subgraph isomorphism problem involves deciding whether a copy of a pattern graph occurs inside a larger target graph. The non-induced version allows extra edges in the target, whilst the induced version does not. Although both variants are NP-complete, algorithms inspired by constraint programming can operate comfortably on many real-world problem instances with thousands of vertices. However, they cannot handle arbitrary instances of this size. We show how to generate " really hard " random instances for subgraph isomorphism problems, which are computationally challenging with a couple of hundred vertices in the target, and only twenty pattern vertices. For the non-induced version of the problem, these instances lie on a satisfiable / unsatisfiable phase transition, whose location we can predict; for the induced variant, much richer behaviour is observed, and constrained-ness gives a better measure of difficulty than does proximity to a phase transition. These results have practical consequences: we explain why the widely researched " filter / verify " indexing technique used in graph databases is founded upon a misunderstanding of the empirical hardness of NP-complete problems, and cannot be beneficial when paired with any reasonable subgraph isomorphism algorithm.
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Dates et versions

hal-01741928 , version 1 (26-03-2018)

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Ciaran Mccreesh, Patrick Prosser, Christine Solnon, James Trimble. When Subgraph Isomorphism is Really Hard, and Why This Matters for Graph Databases. Journal of Artificial Intelligence Research, 2018, 61, pp.723 - 759. ⟨10.1613/jair.5768⟩. ⟨hal-01741928⟩
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