{"id":"https://openalex.org/W2563483334","doi":"https://doi.org/10.23638/dmtcs-20-2-2","title":"On fixed-parameter tractability of the mixed domination problem for graphs with bounded tree-width","display_name":"On fixed-parameter tractability of the mixed domination problem for graphs with bounded tree-width","publication_year":2018,"publication_date":"2018-07-31","ids":{"openalex":"https://openalex.org/W2563483334","doi":"https://doi.org/10.23638/dmtcs-20-2-2","mag":"2563483334"},"language":"en","primary_location":{"id":"doi:10.23638/dmtcs-20-2-2","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-20-2-2","pdf_url":"https://dmtcs.episciences.org/4686/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dmtcs.episciences.org/4686/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014386752","display_name":"M. Rajaati","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Rajaati","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015666782","display_name":"M. R. Hooshmandasl","orcid":"https://orcid.org/0000-0002-3834-3610"},"institutions":[{"id":"https://openalex.org/I112536369","display_name":"Yazd University","ror":"https://ror.org/02x99ac45","country_code":"IR","type":"education","lineage":["https://openalex.org/I112536369"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"M. R. Hooshmandasl","raw_affiliation_strings":["Department of Computer Science, Yazd University, Yazd, Iran","The Laboratory of Quantum Information Processing, Yazd University, Yazd, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Yazd University, Yazd, Iran","institution_ids":["https://openalex.org/I112536369"]},{"raw_affiliation_string":"The Laboratory of Quantum Information Processing, Yazd University, Yazd, Iran","institution_ids":["https://openalex.org/I112536369"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083519582","display_name":"Michael J. Dinneen","orcid":"https://orcid.org/0000-0001-9977-525X"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"M. J. Dinneen","raw_affiliation_strings":["Department of Computer Science, The University of Auckland, Auckland, New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, The University of Auckland, Auckland, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021278463","display_name":"Ali Shakiba","orcid":"https://orcid.org/0000-0002-2253-1166"},"institutions":[{"id":"https://openalex.org/I3020488725","display_name":"Vali Asr University of Rafsanjan","ror":"https://ror.org/056xnk046","country_code":"IR","type":"education","lineage":["https://openalex.org/I3020488725"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"A. Shakiba","raw_affiliation_strings":["Department of Computer Science, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran","institution_ids":["https://openalex.org/I3020488725"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6435,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.69640579,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"vol. 20 no. 2","issue":"Graph Theory","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7408003807067871},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6222338676452637},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6042793989181519},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5575006604194641},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.4926925301551819},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35465285181999207},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.252552330493927},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.2030312418937683},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09346750378608704},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.0403556227684021}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7408003807067871},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6222338676452637},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6042793989181519},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5575006604194641},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.4926925301551819},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35465285181999207},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.252552330493927},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.2030312418937683},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09346750378608704},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0403556227684021}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.23638/dmtcs-20-2-2","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-20-2-2","pdf_url":"https://dmtcs.episciences.org/4686/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1612.08234","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.08234","pdf_url":"https://arxiv.org/pdf/1612.08234","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:f02665842e00453088b3972eb8c81664","is_oa":true,"landing_page_url":"https://doaj.org/article/f02665842e00453088b3972eb8c81664","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science, Vol vol. 20 no. 2, Iss Graph Theory (2018)","raw_type":"article"},{"id":"pmh:oai:researchspace.auckland.ac.nz:2292/34533","is_oa":false,"landing_page_url":"https://hdl.handle.net/2292/34533","pdf_url":null,"source":{"id":"https://openalex.org/S7407055463","display_name":"ResearchSpace (University of Auckland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I154130895","host_organization_name":"University of Auckland","host_organization_lineage":["https://openalex.org/I154130895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Report"},{"id":"pmh:oai:researchspace.auckland.ac.nz:2292/46169","is_oa":true,"landing_page_url":"http://hdl.handle.net/2292/46169","pdf_url":null,"source":{"id":"https://openalex.org/S7407055463","display_name":"ResearchSpace (University of Auckland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I154130895","host_organization_name":"University of Auckland","host_organization_lineage":["https://openalex.org/I154130895"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.23638/dmtcs-20-2-2","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-20-2-2","pdf_url":"https://dmtcs.episciences.org/4686/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320326124","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd Tudom\u00e1nyegyetem","ror":"https://ror.org/01jsq2704"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2563483334.pdf","grobid_xml":"https://content.openalex.org/works/W2563483334.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W182050876","https://openalex.org/W788806422","https://openalex.org/W1493071618","https://openalex.org/W1579510955","https://openalex.org/W1973347908","https://openalex.org/W2002722727","https://openalex.org/W2003272551","https://openalex.org/W2021417413","https://openalex.org/W2028357390","https://openalex.org/W2059372025","https://openalex.org/W2062915396","https://openalex.org/W2070924562","https://openalex.org/W2090187806","https://openalex.org/W2212883086","https://openalex.org/W2765982640","https://openalex.org/W2963745986","https://openalex.org/W3105505998","https://openalex.org/W3141776272"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1810116456","https://openalex.org/W2964174631","https://openalex.org/W4300619607","https://openalex.org/W4321393130","https://openalex.org/W2178269805","https://openalex.org/W2223243427","https://openalex.org/W4306887989","https://openalex.org/W4302375582","https://openalex.org/W2951811902"],"abstract_inverted_index":{"A":[0],"mixed":[1,39,54,60,72,76,86,114],"dominating":[2,55,61,73,87,115],"set":[3,12,62,78,88],"for":[4,89,186],"a":[5,11,43,70,84,90,106,122,146],"graph":[6,44,91,123],"$G":[7],"=":[8],"(V,E)$":[9],"is":[10,28,49,68,81,94,159],"$S\\subseteq":[13],"V":[14],"\\cup":[15,24],"E$":[16],"such":[17],"that":[18,157],"every":[19],"element":[20,35],"$x":[21],"\\in":[22],"(V":[23],"E)":[25],"\\backslash":[26],"S$":[27],"either":[29],"adjacent":[30],"or":[31],"incident":[32],"to":[33,82,96,109,135,145,164,174],"an":[34,98],"of":[36,42,53,57,66,112,121,131,149,192],"$S$.":[37],"The":[38,75],"domination":[40,77],"number":[41],"$G$,":[45],"denoted":[46],"by":[47],"$\\gamma_m(G)$,":[48],"the":[50,64,113,118,171,176,187,190],"minimum":[51,71,85],"cardinality":[52,65],"sets":[56],"$G$.":[58],"Any":[59],"with":[63,124,141,162],"$\\gamma_m(G)$":[67],"called":[69,117],"set.":[74],"(MDS)":[79],"problem":[80,178],"find":[83,110],"$G$":[92],"and":[93,137,139],"known":[95],"be":[97],"NP-complete":[99],"problem.":[100],"In":[101,166],"this":[102],"paper,":[103],"we":[104,168],"present":[105],"novel":[107],"approach":[108],"all":[111],"sets,":[116],"AMDS":[119],"problem,":[120],"bounded":[125],"tree-width":[126],"$tw$.":[127],"Our":[128],"new":[129],"technique":[130],"assigning":[132],"power":[133],"values":[134],"edges":[136],"vertices,":[138],"combining":[140],"dynamic":[142],"programming,":[143],"leads":[144],"fixed-parameter":[147,160],"algorithm":[148,173],"time":[150],"$O(3^{tw^{2}}\\times":[151],"tw^2":[152],"\\times":[153,181],"|V|)$.":[154],"This":[155],"shows":[156],"MDS":[158,177],"tractable":[161],"respect":[163],"tree-width.":[165],"addition,":[167],"theoretically":[169],"improve":[170],"proposed":[172],"solve":[175],"in":[179,189],"$O(6^{tw}":[180],"|V|)$":[182],"time.":[183],"Comment:":[184],"Accepted":[185],"publication":[188],"Journal":[191],"Discrete":[193],"Mathematics":[194],"&":[195],"Theoretical":[196],"Computer":[197],"Science":[198],"(DMTCS).":[199],"25":[200],"pages,":[201],"4":[202,206],"figures,":[203],"17":[204],"tables,":[205],"algorithms":[207]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}