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dc.contributor.authorFoucaud, Florent
dc.contributor.authorGras, Benjamin
dc.contributor.authorPerez, Anthony
hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorSikora, Florian
HAL ID: 742949
ORCID: 0000-0003-2670-6258
dc.date.accessioned2021-10-20T14:43:01Z
dc.date.available2021-10-20T14:43:01Z
dc.date.issued2020
dc.identifier.issn0178-4617
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22057
dc.descriptionUne version préliminaire de cet article a été présentée à la conférence IWOCA’20en
dc.language.isoenen
dc.subjectBroadcast Dominationen
dc.subjectdigraphsen
dc.subject.ddc005en
dc.titleOn the Complexity of Broadcast Domination and Multipacking in Digraphsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the complexity of the two dual covering and packing distance-based problems Broadcast Domination and Multipacking in digraphs. A dominating broadcast of a digraph D is a function f:V(D)→N such that for each vertex v of D, there exists a vertex t with f(t)>0 having a directed path to v of length at most f(t). The cost of f is the sum of f(v) over all vertices v. A multipacking is a set S of vertices of D such that for each vertex v of D and for every integer d, there are at most d vertices from S within directed distance at most d from v. The maximum size of a multipacking of D is a lower bound to the minimum cost of a dominating broadcast of D. Let Broadcast Domination denote the problem of deciding whether a given digraph D has a dominating broadcast of cost at most k, and Multipacking the problem of deciding whether D has a multipacking of size at least k. It is known that Broadcast Domination is polynomial-time solvable for the class of all undirected graphs (that is, symmetric digraphs), while polynomial-time algorithms for Multipacking are known only for a few classes of undirected graphs. We prove that Broadcast Domination and Multipacking are both NP-complete for digraphs, even for planar layered acyclic digraphs of small maximum degree. Moreover, when parameterized by the solution cost/solution size, we show that the problems are respectively W[2]-hard and W[1]-hard. We also show that Broadcast Domination is FPT on acyclic digraphs, and that it does not admit a polynomial kernel for such inputs, unless the polynomial hierarchy collapses to its third level. In addition, we show that both problems are FPT when parameterized by the solution cost/solution size together with the maximum (out-)degree, and as well, by the vertex cover number. Finally, we give for both problems polynomial-time algorithms for some subclasses of acyclic digraphs.en
dc.relation.isversionofjnlnameAlgorithmica
dc.relation.isversionofjnlvol83en
dc.relation.isversionofjnldate2021-09
dc.relation.isversionofjnlpages2651–2677en
dc.relation.isversionofdoi10.1007/s00453-021-00828-5en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelProgrammation, logiciels, organisation des donnéesen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-10-20T14:38:16Z
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