Topological additive numbering of directed acyclic graphs

Autores
Marenco, Javier Leonardo; Mydlarz, Marcelo; Severin, Daniel Esteban
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We propose to study a problem that arises naturally from both TopologicalNumbering of Directed Acyclic Graphs, and Additive Coloring (also knownas Lucky Labeling). LetDbe a digraph andfa labeling of its verticeswith positive integers; denote byS(v) the sum of labels over all neighborsof each vertexv. The labelingfis calledtopological additive numberingifS(u)< S(v) for each arc (u, v) of the digraph. The problem asks to find theminimum numberkfor whichDhas a topological additive numbering withlabels belonging to{1, . . . , k}, denoted byηt(D).We characterize when a digraph has topological additive numberings, givea lower bound forηt(D) and provide an integer programming formulation forour problem. We also present some families for whichηt(D) can be computedin polynomial time. Finally, we prove that this problem isN P-Hard evenwhen its input is restricted to planar bipartite digraphs.
Fil: Marenco, Javier Leonardo. Universidad Nacional de General Sarmiento; Argentina
Fil: Mydlarz, Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento; Argentina
Fil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario; Argentina
Materia
Additive Coloring
Lucky Labeling
Directed Acyclic Graphs
Topological Additive Numbering
Computational Complexity
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/35895
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/35895
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Topological additive numbering of directed acyclic graphsMarenco, Javier LeonardoMydlarz, MarceloSeverin, Daniel EstebanAdditive ColoringLucky LabelingDirected Acyclic GraphsTopological Additive NumberingComputational Complexityhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We propose to study a problem that arises naturally from both TopologicalNumbering of Directed Acyclic Graphs, and Additive Coloring (also knownas Lucky Labeling). LetDbe a digraph andfa labeling of its verticeswith positive integers; denote byS(v) the sum of labels over all neighborsof each vertexv. The labelingfis calledtopological additive numberingifS(u)< S(v) for each arc (u, v) of the digraph. The problem asks to find theminimum numberkfor whichDhas a topological additive numbering withlabels belonging to{1, . . . , k}, denoted byηt(D).We characterize when a digraph has topological additive numberings, givea lower bound forηt(D) and provide an integer programming formulation forour problem. We also present some families for whichηt(D) can be computedin polynomial time. Finally, we prove that this problem isN P-Hard evenwhen its input is restricted to planar bipartite digraphs.Fil: Marenco, Javier Leonardo. Universidad Nacional de General Sarmiento; ArgentinaFil: Mydlarz, Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento; ArgentinaFil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario; ArgentinaElsevier Science2014-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/35895Marenco, Javier Leonardo; Mydlarz, Marcelo; Severin, Daniel Esteban; Topological additive numbering of directed acyclic graphs; Elsevier Science; Information Processing Letters; 115; 2; 9-2014; 199-2020020-0190CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.ipl.2014.09.011info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0020019014001872info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:54:58Zoai:ri.conicet.gov.ar:11336/35895instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:54:58.864CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Topological additive numbering of directed acyclic graphs
title Topological additive numbering of directed acyclic graphs
spellingShingle Topological additive numbering of directed acyclic graphs
Marenco, Javier Leonardo
Additive Coloring
Lucky Labeling
Directed Acyclic Graphs
Topological Additive Numbering
Computational Complexity
title_short Topological additive numbering of directed acyclic graphs
title_full Topological additive numbering of directed acyclic graphs
title_fullStr Topological additive numbering of directed acyclic graphs
title_full_unstemmed Topological additive numbering of directed acyclic graphs
title_sort Topological additive numbering of directed acyclic graphs
dc.creator.none.fl_str_mv Marenco, Javier Leonardo
Mydlarz, Marcelo
Severin, Daniel Esteban
author Marenco, Javier Leonardo
author_facet Marenco, Javier Leonardo
Mydlarz, Marcelo
Severin, Daniel Esteban
author_role author
author2 Mydlarz, Marcelo
Severin, Daniel Esteban
author2_role author
author
dc.subject.none.fl_str_mv Additive Coloring
Lucky Labeling
Directed Acyclic Graphs
Topological Additive Numbering
Computational Complexity
topic Additive Coloring
Lucky Labeling
Directed Acyclic Graphs
Topological Additive Numbering
Computational Complexity
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We propose to study a problem that arises naturally from both TopologicalNumbering of Directed Acyclic Graphs, and Additive Coloring (also knownas Lucky Labeling). LetDbe a digraph andfa labeling of its verticeswith positive integers; denote byS(v) the sum of labels over all neighborsof each vertexv. The labelingfis calledtopological additive numberingifS(u)< S(v) for each arc (u, v) of the digraph. The problem asks to find theminimum numberkfor whichDhas a topological additive numbering withlabels belonging to{1, . . . , k}, denoted byηt(D).We characterize when a digraph has topological additive numberings, givea lower bound forηt(D) and provide an integer programming formulation forour problem. We also present some families for whichηt(D) can be computedin polynomial time. Finally, we prove that this problem isN P-Hard evenwhen its input is restricted to planar bipartite digraphs.
Fil: Marenco, Javier Leonardo. Universidad Nacional de General Sarmiento; Argentina
Fil: Mydlarz, Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento; Argentina
Fil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario; Argentina
description We propose to study a problem that arises naturally from both TopologicalNumbering of Directed Acyclic Graphs, and Additive Coloring (also knownas Lucky Labeling). LetDbe a digraph andfa labeling of its verticeswith positive integers; denote byS(v) the sum of labels over all neighborsof each vertexv. The labelingfis calledtopological additive numberingifS(u)< S(v) for each arc (u, v) of the digraph. The problem asks to find theminimum numberkfor whichDhas a topological additive numbering withlabels belonging to{1, . . . , k}, denoted byηt(D).We characterize when a digraph has topological additive numberings, givea lower bound forηt(D) and provide an integer programming formulation forour problem. We also present some families for whichηt(D) can be computedin polynomial time. Finally, we prove that this problem isN P-Hard evenwhen its input is restricted to planar bipartite digraphs.
publishDate 2014
dc.date.none.fl_str_mv 2014-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/35895
Marenco, Javier Leonardo; Mydlarz, Marcelo; Severin, Daniel Esteban; Topological additive numbering of directed acyclic graphs; Elsevier Science; Information Processing Letters; 115; 2; 9-2014; 199-202
0020-0190
CONICET Digital
CONICET
url http://hdl.handle.net/11336/35895
identifier_str_mv Marenco, Javier Leonardo; Mydlarz, Marcelo; Severin, Daniel Esteban; Topological additive numbering of directed acyclic graphs; Elsevier Science; Information Processing Letters; 115; 2; 9-2014; 199-202
0020-0190
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ipl.2014.09.011
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0020019014001872
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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