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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| Veröffentlicht in: | Theoretical computer science Jg. 1055; S. 115502 |
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Elsevier B.V
09.11.2025
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 115502 |
| Author | Dondi, Riccardo Lafond, Manuel |
| Author_xml | – sequence: 1 givenname: Riccardo orcidid: 0000-0002-6124-2965 surname: Dondi fullname: Dondi, Riccardo email: riccardo.dondi@unibg.it organization: Università degli Studi di Bergamo, Italy – sequence: 2 givenname: Manuel orcidid: 0000-0002-5305-7372 surname: Lafond fullname: Lafond, Manuel email: manuel.lafond@usherbrooke.ca organization: Université de Sherbrooke, Canada |
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| Cites_doi | 10.4086/toc.2015.v011a007 10.1016/j.ipl.2014.10.005 10.1140/epjb/e2015-60657-4 10.1007/s13721-022-00406-x 10.1613/jair.1.11509 10.1016/j.tcs.2020.11.021 10.1006/jcss.2002.1829 10.3390/a11040052 10.1016/j.jcss.2024.103548 10.1016/j.jcss.2021.04.001 10.1093/bioinformatics/btad230 10.1080/15427951.2016.1177801 10.1016/j.jcss.2024.103596 10.1016/j.tcs.2008.09.065 10.1016/j.tcs.2022.12.007 10.1016/j.tcs.2010.12.005 10.1145/1150334.1150336 |
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| Keywords | Temporal graphs Approximation complexity Arborescence Graph algorithms Parameterized complexity |
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