Abstract
When information is (implicitly or explicitly) linked in its own nature, and is modeled as a network, retrieving patterns can benefit from this linked structure. In networks, “graphlets” (connected induced subgraphs of a given size k) are the counterparts of textual n-grams, as their frequency and shape can give powerful insights in the structure of a network and the role of its nodes. Differently from n-grams, the number of graphlets increases dramatically with their size k. We aim to push the exact enumeration of graphlets as far as possible, as enumeration (contrary to counting or approximation) gives the end-user the flexibility of arbitrary queries and restrictions on the graphlets found. For this, we exploit combinatorial and cache-efficient design strategies to cut the computational cost. The resulting algorithm CAGE (Cache-Aware Graphlet Enumeration) outperforms existing enumeration strategies by at least an order of magnitude, exhibiting a low number of L1-L2-L3 cache misses in the CPU. It is also competitive with the fastest known counting algorithms, without having their limitations on k.
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Notes
- 1.
Here \(G \setminus \{u\}\) is G without u and its incident edges.
- 2.
We are not directly controlling the cache, but rather allowing the algorithm to run cache-friendly by making standard assumptions on the associative cache [8].
- 3.
This idea can be generalized to \(k-4\), \(k-5\), and so on, but there is no payoff going further than \(k-3\) in practice as there are too many cases to handle.
- 4.
- 5.
This timeout is due to the size of the data gathered by VTune, which grows quickly over time.
- 6.
i.e. the runtime raised a bad_alloc exception or a segmentation fault while reading the input graph.
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Acknowledgements
Work partially supported by MIUR project n. 20174LF3T8 Algorithms for Harnessing networked Data (AHeAD).
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Conte, A., Grossi, R., Rucci, D. (2023). CAGE: Cache-Aware Graphlet Enumeration. In: Nardini, F.M., Pisanti, N., Venturini, R. (eds) String Processing and Information Retrieval. SPIRE 2023. Lecture Notes in Computer Science, vol 14240. Springer, Cham. https://doi.org/10.1007/978-3-031-43980-3_11
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