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Enumerating Subgraphs of Constant Sizes in External Memory

Authors Shiyuan Deng, Francesco Silvestri, Yufei Tao

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Author Details

Shiyuan Deng
  • The Chinese University of Hong Kong, China
Francesco Silvestri
  • University of Padova, Italy
Yufei Tao
  • The Chinese University of Hong Kong, China

Funding

Shiyuan Deng and Yufei Tao were supported in part by GRF Projects 14207820, 14203421, and 14222822 from HKRGC. Francesco Silvestri was supported in part by PRIN 20174LF3T8 AHeAD and Uni-Impresa Big-Mobility projects, and by the Italian National Center for HPC, Big Data, and Quantum Computing.

Cite As Get BibTex

Shiyuan Deng, Francesco Silvestri, and Yufei Tao. Enumerating Subgraphs of Constant Sizes in External Memory. In 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 255, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ICDT.2023.4

Abstract

We present an indivisible I/O-efficient algorithm for subgraph enumeration, where the objective is to list all the subgraphs of a massive graph G : = (V, E) that are isomorphic to a pattern graph Q having k = O(1) vertices. Our algorithm performs O((|E|^{k/2})/(M^{{k/2}-1} B) log_{M/B}(|E|/B) + (|E|^ρ)/(M^{ρ-1} B) I/Os with high probability, where ρ is the fractional edge covering number of Q (it always holds ρ ≥ k/2, regardless of Q), M is the number of words in (internal) memory, and B is the number of words in a disk block. Our solution is optimal in the class of indivisible algorithms for all pattern graphs with ρ > k/2. When ρ = k/2, our algorithm is still optimal as long as M/B ≥ (|E|/B)^ε for any constant ε > 0.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Information systems → Join algorithms
Keywords
  • Subgraph Enumeration
  • Conjunctive Queries
  • External Memory
  • Algorithms

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