{"id":"https://openalex.org/W2567413373","doi":"https://doi.org/10.1137/15m1039821","title":"Weighted Efficient Domination for $P_5$-Free and $P_6$-Free Graphs","display_name":"Weighted Efficient Domination for $P_5$-Free and $P_6$-Free Graphs","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2567413373","doi":"https://doi.org/10.1137/15m1039821","mag":"2567413373"},"language":"en","primary_location":{"id":"doi:10.1137/15m1039821","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1039821","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085372854","display_name":"Andreas Brandst\u00e4dt","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andreas Brandst\u00e4dt","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040644152","display_name":"Raffaele Mosca","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raffaele Mosca","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8023,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.8735828,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"4","first_page":"2288","last_page":"2303"},"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":0.9948999881744385,"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":0.994700014591217,"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/combinatorics","display_name":"Combinatorics","score":0.8117863535881042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7887524366378784},{"id":"https://openalex.org/keywords/maximal-independent-set","display_name":"Maximal independent set","score":0.6048589944839478},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.5851500034332275},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5845276117324829},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.560259222984314},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.463541716337204},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4550917148590088},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.45498764514923096},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.4167792797088623},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3555462956428528},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.26041722297668457}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8117863535881042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7887524366378784},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.6048589944839478},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.5851500034332275},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5845276117324829},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.560259222984314},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.463541716337204},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4550917148590088},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.45498764514923096},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.4167792797088623},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3555462956428528},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.26041722297668457}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1039821","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1039821","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1541111991","https://openalex.org/W1970348285","https://openalex.org/W1973229660","https://openalex.org/W1973932399","https://openalex.org/W2010608390","https://openalex.org/W2064721098","https://openalex.org/W2170633983"],"related_works":["https://openalex.org/W300018836","https://openalex.org/W2029336174","https://openalex.org/W3037291746","https://openalex.org/W3164644441","https://openalex.org/W2906881967","https://openalex.org/W2935770235","https://openalex.org/W2991587872","https://openalex.org/W1973932399","https://openalex.org/W3004945501","https://openalex.org/W3118753906"],"abstract_inverted_index":{"In":[0],"a":[1,6,131],"finite":[2],"undirected":[3],"graph":[4],"$G=(V,E)$,":[5],"vertex":[7,19,46],"$v":[8,36],"\\in":[9,37],"V$":[10,23,38],"dominates":[11],"itself":[12],"and":[13,72,99,137],"its":[14],"neighbors":[15],"in":[16,41,62,74,108,161],"$G$.":[17],"A":[18],"set":[20,28],"$D":[21],"\\subseteq":[22],"is":[24,39,64,106,135,159,183],"an":[25,60,141],"efficient":[26],"dominating":[27],"(e.d.s.":[29],"for":[30,56,69,77,88,111,119,126,147,164,172,180],"short)":[31],"of":[32,47,59,91,175],"$G$":[33,42],"if":[34],"every":[35],"dominated":[40],"by":[43,130],"exactly":[44],"one":[45],"$D$.":[48],"The":[49,80,178],"Efficient":[50],"Domination":[51],"(ED)":[52],"problem,":[53],"which":[54,134,167],"asks":[55],"the":[57,84,89,120,173],"existence":[58],"e.d.s.":[61],"$G$,":[63],"known":[65],"to":[66],"be":[67],"NP-complete":[68],"$P_7$-free":[70],"graphs":[71,166,182],"solvable":[73,107,160],"polynomial":[75,109],"time":[76,110,145,163],"$P_5$-free":[78,165,181],"graphs.":[79,95,128,152],"$P_6$-free":[81,112,127,151],"case":[82],"was":[83],"last":[85],"open":[86,170],"question":[87,171],"complexity":[90,174],"ED":[92,105,149,158],"on":[93,115,150,185],"$F$-free":[94],"Recently,":[96],"Lokshtanov,":[97],"Pilipczuk,":[98],"van":[100],"Leeuwen":[101],"showed":[102],"that":[103,156],"weighted":[104,148,157],"graphs,":[113],"based":[114,184],"their":[116],"quasi-polynomial":[117],"algorithm":[118],"Maximum":[121],"Weight":[122],"Independent":[123],"Set":[124],"problem":[125],"Independently,":[129],"direct":[132],"approach":[133],"simpler":[136],"faster,":[138],"we":[139,154],"found":[140],"${\\cal":[142],"O}(n^5":[143],"m)$":[144],"solution":[146],"Moreover,":[153],"show":[155],"linear":[162],"solves":[168],"another":[169],"(weighted)":[176],"ED.":[177],"result":[179],"modular":[186],"decomposition.":[187]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
