{"id":"https://openalex.org/W2039826584","doi":"https://doi.org/10.3390/a6010043","title":"Computational Study on a PTAS for Planar Dominating Set Problem","display_name":"Computational Study on a PTAS for Planar Dominating Set Problem","publication_year":2013,"publication_date":"2013-01-21","ids":{"openalex":"https://openalex.org/W2039826584","doi":"https://doi.org/10.3390/a6010043","mag":"2039826584"},"language":"en","primary_location":{"id":"doi:10.3390/a6010043","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a6010043","pdf_url":"https://www.mdpi.com/1999-4893/6/1/43/pdf?version=1358865028","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/6/1/43/pdf?version=1358865028","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062344814","display_name":"Marjan Marzban","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Marjan Marzban","raw_affiliation_strings":["School of Computing Science, Simon Fraser University, Burnaby BC, V5A 1S6, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computing Science, Simon Fraser University, Burnaby BC, V5A 1S6, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5104064156","display_name":"Qian\u2010Ping Gu","orcid":"https://orcid.org/0009-0003-6242-3404"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Qian-Ping Gu","raw_affiliation_strings":["School of Computing Science, Simon Fraser University, Burnaby BC, V5A 1S6, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computing Science, Simon Fraser University, Burnaby BC, V5A 1S6, Canada","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5104064156"],"corresponding_institution_ids":["https://openalex.org/I18014758"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.7472,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73498391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"6","issue":"1","first_page":"43","last_page":"59"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9998000264167786,"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/T12288","display_name":"Optimization and Search Problems","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/dominating-set","display_name":"Dominating set","score":0.7593907713890076},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6820277571678162},{"id":"https://openalex.org/keywords/polynomial-time-approximation-scheme","display_name":"Polynomial-time approximation scheme","score":0.6693713665008545},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.6548136472702026},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6520516872406006},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5939986705780029},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45106273889541626},{"id":"https://openalex.org/keywords/planar-straight-line-graph","display_name":"Planar straight-line graph","score":0.4454444944858551},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4389106035232544},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4358150064945221},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4260328710079193},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.4193274676799774},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38814276456832886},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17680701613426208},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.1701294481754303},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16316789388656616},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.08579835295677185},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07153579592704773}],"concepts":[{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.7593907713890076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6820277571678162},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.6693713665008545},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.6548136472702026},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6520516872406006},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5939986705780029},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45106273889541626},{"id":"https://openalex.org/C131930043","wikidata":"https://www.wikidata.org/wiki/Q7200964","display_name":"Planar straight-line graph","level":5,"score":0.4454444944858551},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4389106035232544},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4358150064945221},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4260328710079193},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.4193274676799774},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38814276456832886},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17680701613426208},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.1701294481754303},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16316789388656616},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.08579835295677185},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07153579592704773},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a6010043","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a6010043","pdf_url":"https://www.mdpi.com/1999-4893/6/1/43/pdf?version=1358865028","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:05fa9f793d734f728e795407d32f58bd","is_oa":true,"landing_page_url":"https://doaj.org/article/05fa9f793d734f728e795407d32f58bd","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 6, Iss 1, Pp 43-59 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a6010043","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a6010043","pdf_url":"https://www.mdpi.com/1999-4893/6/1/43/pdf?version=1358865028","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2039826584.pdf","grobid_xml":"https://content.openalex.org/works/W2039826584.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1493071618","https://openalex.org/W1530753374","https://openalex.org/W1558829011","https://openalex.org/W1582963151","https://openalex.org/W1983156760","https://openalex.org/W1987374783","https://openalex.org/W2011039300","https://openalex.org/W2019137761","https://openalex.org/W2025536756","https://openalex.org/W2040924621","https://openalex.org/W2047871605","https://openalex.org/W2048794017","https://openalex.org/W2052812513","https://openalex.org/W2065482951","https://openalex.org/W2079444475","https://openalex.org/W2084507343","https://openalex.org/W2093762675","https://openalex.org/W2120560389","https://openalex.org/W2143996311","https://openalex.org/W2144599263","https://openalex.org/W2144809360","https://openalex.org/W2156760067","https://openalex.org/W2163428398","https://openalex.org/W2477122060","https://openalex.org/W2799349239","https://openalex.org/W2913688336","https://openalex.org/W4232845306","https://openalex.org/W6634856957"],"related_works":["https://openalex.org/W1491152805","https://openalex.org/W2081273953","https://openalex.org/W3002061974","https://openalex.org/W2951173809","https://openalex.org/W4291736767","https://openalex.org/W2009558719","https://openalex.org/W165147621","https://openalex.org/W2002953601","https://openalex.org/W2119795420","https://openalex.org/W2001770522"],"abstract_inverted_index":{"The":[0],"dominating":[1,69,95,112],"set":[2,70,96,113],"problem":[3,8],"is":[4,47,61,86,162],"a":[5,24,38,62,107,148],"core":[6],"NP-hard":[7,41],"in":[9,43,143],"combinatorial":[10],"optimization":[11],"and":[12,15],"graph":[13,27,118,133],"theory,":[14],"has":[16,123],"many":[17],"important":[18],"applications.":[19],"Baker":[20],"[JACM":[21],"41,1994]":[22],"introduces":[23],"k-outer":[25,116],"planar":[26,44,68,94,111,117,132],"decomposition-based":[28],"framework":[29,51,85,104],"for":[30,37,66,92,109],"designing":[31],"polynomial":[32],"time":[33],"approximation":[34,76,125,140],"scheme":[35],"(PTAS)":[36],"class":[39],"of":[40,83,102],"problems":[42],"graphs.":[45],"It":[46],"mentioned":[48,81],"that":[49,74,158],"the":[50,67,75,80,84,93,100,103,110,120,135,139,152,159],"can":[52],"be":[53],"applied":[54],"to":[55,105],"obtain":[56],"an":[57,124],"O(2ckn)":[58],"time,":[59],"c":[60],"constant,":[63],"(1+1/k)-approximation":[64],"algorithm":[65],"problem.":[71,97,114],"We":[72,98,146],"show":[73,157],"ratio":[77,126,141],"achieved":[78],"by":[79,89],"application":[82,101],"not":[87],"bounded":[88],"any":[90],"constant":[91],"modify":[99],"give":[106],"PTAS":[108,122,137,161],"With":[115],"decompositions,":[119,134],"modified":[121,136,153,160],"(1":[127],"+":[128],"2/k).":[129],"Using":[130],"2k-outer":[131],"achieves":[138],"(1+1/k)":[142],"O(22ckn)":[144],"time.":[145],"report":[147],"computational":[149],"study":[150],"on":[151],"PTAS.":[154],"Our":[155],"results":[156],"practical.":[163]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}