{"id":"https://openalex.org/W1589219240","doi":"https://doi.org/10.1007/s00453-017-0401-6","title":"A Polynomial Kernel for Trivially Perfect Editing","display_name":"A Polynomial Kernel for Trivially Perfect Editing","publication_year":2017,"publication_date":"2017-12-28","ids":{"openalex":"https://openalex.org/W1589219240","doi":"https://doi.org/10.1007/s00453-017-0401-6","mag":"1589219240"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-017-0401-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-017-0401-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-017-0401-6.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-017-0401-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064442594","display_name":"P\u00e5l Gr\u00f8n\u00e5s Drange","orcid":"https://orcid.org/0000-0001-7228-6640"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"P\u00e5l Gr\u00f8n\u00e5s Drange","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway","Univ.\u00a0Bergen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Univ.\u00a0Bergen","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000479623","display_name":"Micha\u0142 Pilipczuk","orcid":"https://orcid.org/0000-0001-7891-1988"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Micha\u0142 Pilipczuk","raw_affiliation_strings":["Institute of Informatics, University of Warsaw, Warsaw, Poland","Univ.\u00a0Warsaw"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Univ.\u00a0Warsaw","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000479623"],"corresponding_institution_ids":["https://openalex.org/I4654613"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.4252,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.61640885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"80","issue":"12","first_page":"3481","last_page":"3524"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"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":0.9980999827384949,"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":0.9976000189781189,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9966999888420105,"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/kernelization","display_name":"Kernelization","score":0.9540437459945679},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7284033298492432},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6666731238365173},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6625890731811523},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5522204041481018},{"id":"https://openalex.org/keywords/perfect-power","display_name":"Perfect power","score":0.5191406607627869},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.4835464656352997},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.472557008266449},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45714572072029114},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4421965777873993},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"Polynomial kernel","score":0.42602914571762085},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.2149423360824585},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1865098476409912},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1849660873413086}],"concepts":[{"id":"https://openalex.org/C207225210","wikidata":"https://www.wikidata.org/wiki/Q1759539","display_name":"Kernelization","level":3,"score":0.9540437459945679},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7284033298492432},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6666731238365173},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6625890731811523},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5522204041481018},{"id":"https://openalex.org/C93446932","wikidata":"https://www.wikidata.org/wiki/Q1972803","display_name":"Perfect power","level":2,"score":0.5191406607627869},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4835464656352997},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.472557008266449},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45714572072029114},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4421965777873993},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.42602914571762085},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.2149423360824585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1865098476409912},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1849660873413086},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00453-017-0401-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-017-0401-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-017-0401-6.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00453-017-0401-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-017-0401-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-017-0401-6.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3207356259","display_name":null,"funder_award_id":"2007\u20132013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6775816958","display_name":null,"funder_award_id":"FP/2007-2013","funder_id":"https://openalex.org/F4320323078","funder_display_name":"Universitetet i Bergen"},{"id":"https://openalex.org/G7546946110","display_name":null,"funder_award_id":"FP/2007-2013)/ERC","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7723633313","display_name":null,"funder_award_id":"UMO-2013/11/D/ST6/03073","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G8174586523","display_name":null,"funder_award_id":"267959","funder_id":"https://openalex.org/F4320334960","funder_display_name":"Seventh Framework Programme"},{"id":"https://openalex.org/G896728979","display_name":null,"funder_award_id":"FP/2007/2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"},{"id":"https://openalex.org/F4320323078","display_name":"Universitetet i Bergen","ror":"https://ror.org/03zga2b32"},{"id":"https://openalex.org/F4320323873","display_name":"Uniwersytet Warszawski","ror":"https://ror.org/039bjqg32"},{"id":"https://openalex.org/F4320334960","display_name":"Seventh Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1589219240.pdf","grobid_xml":"https://content.openalex.org/works/W1589219240.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W938002210","https://openalex.org/W1570425181","https://openalex.org/W1674929459","https://openalex.org/W1754878559","https://openalex.org/W1836501071","https://openalex.org/W1897023681","https://openalex.org/W1971361630","https://openalex.org/W1985427743","https://openalex.org/W1995725694","https://openalex.org/W1996472240","https://openalex.org/W1998552318","https://openalex.org/W2000763343","https://openalex.org/W2008978934","https://openalex.org/W2014363582","https://openalex.org/W2020913456","https://openalex.org/W2028651304","https://openalex.org/W2034115935","https://openalex.org/W2048845385","https://openalex.org/W2051576576","https://openalex.org/W2059401572","https://openalex.org/W2059608229","https://openalex.org/W2088722899","https://openalex.org/W2104894563","https://openalex.org/W2115674935","https://openalex.org/W2126383829","https://openalex.org/W2144050783","https://openalex.org/W2155453078","https://openalex.org/W2158584754","https://openalex.org/W2168123742","https://openalex.org/W2168488683","https://openalex.org/W2170633983","https://openalex.org/W2234496216","https://openalex.org/W2243582562","https://openalex.org/W2253699097","https://openalex.org/W2271457994","https://openalex.org/W2277785367","https://openalex.org/W2332963763","https://openalex.org/W2570366614","https://openalex.org/W2592570088","https://openalex.org/W2908014032","https://openalex.org/W2912532202","https://openalex.org/W2913688336","https://openalex.org/W2949581077","https://openalex.org/W3150848178","https://openalex.org/W4233756358","https://openalex.org/W4292230561"],"related_works":["https://openalex.org/W2381408042","https://openalex.org/W2425261484","https://openalex.org/W33845589","https://openalex.org/W189387296","https://openalex.org/W4388276051","https://openalex.org/W2161286454","https://openalex.org/W2964273883","https://openalex.org/W2355184605","https://openalex.org/W2122202324","https://openalex.org/W4382583004"],"abstract_inverted_index":{"We":[0,108],"give":[1],"a":[2,25],"kernel":[3,85,105],"with":[4],"$$O(k^7)$$":[5],"vertices":[6],"for":[7,69,80,100,157],"Trivially":[8,71,75,113,121],"Perfect":[9,72,76,114,122],"Editing,":[10],"the":[11,61,66,81,101,133,143,146,152,158],"problem":[12],"of":[13,63,65,112,145,151,160],"adding":[14],"or":[15],"removing":[16],"at":[17],"most":[18],"k":[19],"edges":[20],"in":[21,32,128],"order":[22],"to":[23,120],"make":[24],"given":[26,87],"graph":[27],"trivially":[28,161],"perfect.":[29],"This":[30],"answers":[31],"affirmative":[33],"an":[34,83],"open":[35],"question":[36],"posed":[37],"by":[38,47,88,116],"Nastos":[39],"and":[40,46,74,148],"Gao":[41],"(Soc":[42],"Netw":[43],"35(3):439\u2013450,":[44],"2013),":[45],"Liu":[48],"et":[49],"al.":[50],"(Tsinghua":[51],"Sci":[52],"Technol":[53],"19(4):346\u2013357,":[54],"2014).":[55],"Our":[56],"general":[57],"technique":[58],"implies":[59],"also":[60],"existence":[62],"kernels":[64],"same":[67],"size":[68],"related":[70],"Completion":[73],"Deletion":[77],"problems.":[78],"Whereas":[79],"former":[82],"$$O(k^3)$$":[84],"was":[86,106],"Guo":[89],"(in:":[90],"ISAAC":[91],"2007,":[92],"LNCS,":[93],"vol":[94],"4835,":[95],"Springer,":[96],"pp":[97],"915\u2013926,":[98],"2007),":[99],"latter":[102],"no":[103],"polynomial":[104],"known.":[107],"complement":[109],"our":[110],"study":[111],"Editing":[115],"proving":[117],"that,":[118],"contrary":[119],"Completion,":[123],"it":[124],"cannot":[125],"be":[126],"solved":[127],"time":[129,135],"$$2^{o(k)}\\cdot":[130],"n^{O(1)}$$":[131],"unless":[132],"exponential":[134],"hypothesis":[136],"fails.":[137],"In":[138],"this":[139],"manner":[140],"we":[141],"complete":[142],"picture":[144],"parameterized":[147],"kernelization":[149],"complexity":[150],"classic":[153],"edge":[154],"modification":[155],"problems":[156],"class":[159],"perfect":[162],"graphs.":[163]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}