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Spanner Enumeration for Temporal Graphs

Authors Kazuhiro Kurita , Andrea Marino , Jason Schoeters , Takeaki Uno

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph enumeration
  • Theory of computation → Sparsification and spanners
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Problems, reductions and completeness
  • Networks → Network dynamics
Keywords
  • temporal graphs
  • temporal spanners
  • one-to-all connectivity
  • all-to-all connectivity enumeration
  • NP-completeness
  • Dual-hardness
  • binary partition tree
  • flashlight search
  • polynomial delay

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Abstract

A spanner of a temporal graph is a subset of edges that preserves connectivity over time between vertices. A minimal spanner is one in which no additional edges can be removed without breaking this connectivity. Our focus is on enumerating minimal spanners for a given temporal graph. We explore several variations of this problem based on the type of connectivity that must be maintained, ranging from one-to-all connectivity to one-to-all-to-one, many-to-all, and finally all-to-all connectivity. We establish that these problems become progressively harder: (i) We present a polynomial-delay enumeration algorithm for one-to-all connectivity; (ii) We prove Dual-hardness for both one-to-all-to-one and many-to-all connectivity, even in the restricted case of two-to-all; (iii) Finally, for all-to-all connectivity, we show that enumeration cannot be performed in output-polynomial time unless P = NP.

Cite As Get BibTex

Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno. Spanner Enumeration for Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.9

Author Details

Kazuhiro Kurita
  • Nagoya University, Nagoya, Japan
Andrea Marino
  • Dipartimento di Statistica, Informatica, Applicazioni, Università degli Studi di Firenze, Italy
Jason Schoeters
  • Dipartimento di Statistica, Informatica, Applicazioni, Università degli Studi di Firenze, Italy
Takeaki Uno
  • National Institute of Informatics, Tokyo, Japan

Funding

  • Kurita, Kazuhiro: JSPS Kakenhi Grant Numbers JP21K17812, JP23K24806, and JP25K21273, and JST ACT-X Grant Number JPMJAX2105.
  • Marino, Andrea: 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.
  • Schoeters, Jason: PRIN PNRR Project n. P2022NZPJA - DLT-FRUIT: A user centered framework for facilitating DLTs FRUITion.

Acknowledgements

We would like to thank Lapo Cioni for the joining in the verification of constructions and proofs during coffee breaks.

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