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Subgraph Enumeration in Optimal I/O Complexity

Authors Shiyuan Deng, Yufei Tao

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Author Details

Shiyuan Deng
  • The Chinese University of Hong Kong, China
Yufei Tao
  • The Chinese University of Hong Kong, China

Funding

This work was supported in part by GRF projects 14207820, 14203421, and 14222822 from HKRGC.

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Shiyuan Deng and Yufei Tao. Subgraph Enumeration in Optimal I/O Complexity. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICDT.2024.21

Abstract

Given a massive data graph G = (V, E) and a small pattern graph Q, the goal of subgraph enumeration is to list all the subgraphs of G isomorphic to Q. In the external memory (EM) model, it is well-known that every indivisible algorithm must perform Ω({|E|^ρ}/{M^{ρ-1} B}) I/Os in the worst case, where M represents the number of words in (internal) memory, B denotes the number of words in a disk block, and ρ is the fractional edge covering number of Q. It has been a longstanding open problem to design an algorithm to match this lower bound. The state of the art is an algorithm in ICDT'23 that achieves an I/O complexity of O({|E|^ρ}/{M^{ρ-1} B} log_{M/B} |E|/B) with high probability. In this paper, we remove the log_{M/B} |E|/B factor, thereby settling the open problem when randomization is permitted.

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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