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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/35895
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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 Técnicas2025-09-29T10:22:12Zoai: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:34982025-09-29 10:22:12.718CONICET 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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.070432 |