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Designing Output Sensitive Algorithms for Subgraph Enumeration

Authors Alessio Conte , Kazuhiro Kurita , Andrea Marino , Giulia Punzi , Takeaki Uno , Kunihiro Wasa

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph enumeration
  • Mathematics of computing → Graph algorithms
Keywords
  • Graph algorithms
  • Graph enumeration
  • Output sensitive enumeration

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Abstract

The enumeration of all subgraphs respecting some structural property is a fundamental task in theoretical computer science, with practical applications in many branches of data mining and network analysis. It is often of interest to only consider solutions (subgraphs) that are maximal under inclusion, and to achieve output-sensitive complexity, i.e., bounding the running time with respect to the number of subgraphs produced. In this paper, we provide a survey of techniques for designing output-sensitive algorithms for subgraph enumeration, including partition-based approaches such as flashlight search, solution-graph traversal methods such as reverse search, and cost amortization strategies such as push-out amortization. We also briefly discuss classes of efficiency, hardness of enumeration, and variants such as approximate enumeration. The paper is meant as an accessible handbook for learning the basics of the field and as a practical reference for selecting state-of-the-art subgraph enumeration strategies fitting to one’s needs.

Cite As Get BibTex

Alessio Conte, Kazuhiro Kurita, Andrea Marino, Giulia Punzi, Takeaki Uno, and Kunihiro Wasa. Designing Output Sensitive Algorithms for Subgraph Enumeration. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 19:1-19:40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.Grossi.19

Author Details

Alessio Conte
  • University of Pisa, Italy
Kazuhiro Kurita
  • Nagoya University, Japan
Andrea Marino
  • University of Florence, Italy
Giulia Punzi
  • University of Pisa, Italy
Takeaki Uno
  • National Institute of Informatics, Tokyo, Japan
Kunihiro Wasa
  • Hosei University, Tokyo, Japan

Funding

  • Conte, Alessio: Partially supported by MUR PRIN 2022 project EXPAND: scalable algorithms for EXPloratory Analyses of heterogeneous and dynamic Networked Data (#2022TS4Y3N).
  • Kurita, Kazuhiro: Partially supported by Kakenhi JP23K24806, JP25K00136, JP25K21273, and JP25K03080.
  • Marino, Andrea: Partially supported by Italian PNRR CN4 Centro Nazionale per la Mobilità Sostenibile, NextGeneration EU - CUP, B13C22001000001. MUR of Italy, under PRIN Project n. 2022ME9Z78 - NextGRAAL: Next-generation algorithms for constrained GRAph visuALization, PRIN PNRR Project n. P2022NZPJA - DLT-FRUIT: A user centered framework for facilitating DLTs FRUITion.
  • Punzi, Giulia: Supported by the Italian Ministry of Research, under the complementary actions to the NRRP "Fit4MedRob - Fit for Medical Robotics" Grant (#PNC0000007).

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