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On the Complexity of Temporal Arborescence Reconfiguration

Authors Riccardo Dondi , Manuel Lafond

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Riccardo Dondi
  • Università degli Studi di Bergamo, Italy
Manuel Lafond
  • Université de Sherbrooke, Canada

Acknowledgements

The authors thank the anonymous reviewers for their comments on the paper. The authors also thank Shun-ichi Maezawa for introducing the problem to the authors.

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Riccardo Dondi and Manuel Lafond. On the Complexity of Temporal Arborescence Reconfiguration. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SAND.2024.10

Abstract

We analyze the complexity of Arborescence Reconfiguration on temporal digraphs (Temporal Arborescence Reconfiguration). The problem, given two temporal arborescences in a temporal digraph, asks for the minimum number of arc flips, i.e. arc exchanges, that result in a sequence of temporal arborescences that transforms one into the other. We analyze the complexity of the problem, taking into account also its approximation and parameterized complexity, even in restricted cases. First, we solve an open problem showing that Temporal Arborescence Reconfiguration is NP-hard for two timestamps. Then we show that even if the two temporal arborescences differ only by two arcs, then the problem is not approximable within factor bln|V(D)|, for any constant 0 < b < 1, where V(D) is the set of vertices of the temporal arborescences. Finally, we prove that Temporal Arborescence Reconfiguration is W[1]-hard when parameterized by the number of arc flips needed to transform one temporal arborescence into the other.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graph theory
Keywords
  • Arborescence
  • Temporal Graphs
  • Graph Algorithms
  • Parameterized Complexity
  • Approximation Complexity

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