On the complexity of temporal arborescence reconfiguration

In this contribution we study the 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 arbor...

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Bibliographic Details
Published in:Theoretical computer science Vol. 1055; p. 115502
Main Authors: Dondi, Riccardo, Lafond, Manuel
Format: Journal Article
Language:English
Published: Elsevier B.V 09.11.2025
Subjects:
Approximation complexity
Arborescence
Graph algorithms
Parameterized complexity
Temporal graphs
Temporal graphs
Approximation complexity
Arborescence
Graph algorithms
Parameterized complexity
ISSN:0304-3975
Online Access:Get full text
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Summary:In this contribution we study the 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 transforming 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 pairs of 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.
ISSN:0304-3975
DOI:10.1016/j.tcs.2025.115502