65 lines
2.5 KiB
Markdown
65 lines
2.5 KiB
Markdown
# `vf2` — VF2 subgraph isomorphism algorithm in Rust
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This crate implements the VF2 subgraph isomorphism algorithm [1].
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It can find
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[graph isomorphisms](https://en.wikipedia.org/wiki/Graph_isomorphism),
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[subgraph isomorphisms](https://en.wikipedia.org/wiki/Subgraph_isomorphism_problem),
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and [induced subgraph isomorphisms](https://en.wikipedia.org/wiki/Induced_subgraph_isomorphism_problem).
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Graphs can be directed or undirected.
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# Features
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- [x] Enumerate graph isomorphisms
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- [x] Enumerate subgraph isomorphisms
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- [x] Enumerate induced subgraph isomorphisms
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- [x] Support directed graphs
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- [x] Support undirected graphs
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- [x] Support disconnected graphs
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- [x] Support node labels
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- [x] Support edge labels
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- [x] Graph trait
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# What is subgraph isomorphism?
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A graph is a structure consisting of a set of objects where some pairs of objects are connected. A graph isomorphism is
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a one-to-one correspondence between two graphs such that objects connected in one are also connected in the other.
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### Graph isomorphism
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For two graphs to be isomorphic, there must be a one-to-one correspondence between nodes such that neighbors in one are
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also neighbors in the other. The query and data graphs in the following image are isomorphic.
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### Subgraph isomorphism
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It is often desirable to find instances of one graph within another. To do this, we search for subgraph isomorphisms. A
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subgraph isomorphism is when one graph is isomorphic to a subgraph of another. There are two subgraph isomorphisms in
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the following image.
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### Induced subgraph isomorphism
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An induced subgraph isomorphism is the same as a subgraph isomorphism except that the subgraph must be induced. Edges in
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the data subgraph must also exist in the query graph.
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# Remaining work
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- [ ] Implement VF2 cutting rules
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- [ ] Implement VF2++ (only VF2 implemented so far)
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# References
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[1] L. P. Cordella, P. Foggia, C. Sansone, and M. Vento,
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“A (sub)graph isomorphism algorithm for matching large graphs,”
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IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 10, pp. 1367–1372,
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Oct. 2004, doi: https://doi.org/10.1109/tpami.2004.75.
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[2] A. Jüttner and P. Madarasi,
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“VF2++—An improved subgraph isomorphism algorithm,”
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Discrete Applied Mathematics, vol. 242, pp. 69–81,
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Jun. 2018, doi: https://doi.org/10.1016/j.dam.2018.02.018.
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