{"id":"https://openalex.org/W2125332637","doi":"https://doi.org/10.1007/978-3-662-53174-7_5","title":"Complexity of Secure Sets","display_name":"Complexity of Secure Sets","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2125332637","doi":"https://doi.org/10.1007/978-3-662-53174-7_5","mag":"2125332637","pmid":"https://pubmed.ncbi.nlm.nih.gov/29937611"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-662-53174-7_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-53174-7_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00453-017-0358-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071014536","display_name":"Bernhard Bliem","orcid":"https://orcid.org/0000-0002-2898-2830"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Bernhard Bliem","raw_affiliation_strings":["Institute of Information Systems 184/2, TU Wien, Favoritenstrasse 9-11, 1040 Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Information Systems 184/2, TU Wien, Favoritenstrasse 9-11, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006053030","display_name":"Stefan Woltran","orcid":"https://orcid.org/0000-0003-1594-8972"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Stefan Woltran","raw_affiliation_strings":["Institute of Information Systems 184/2, TU Wien, Favoritenstrasse 9-11, 1040 Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Information Systems 184/2, TU Wien, Favoritenstrasse 9-11, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071014536"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0080366,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"80","issue":"10","first_page":"2909","last_page":"2940"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":1.0,"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":1.0,"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":0.9995999932289124,"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":0.9994999766349792,"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/parameterized-complexity","display_name":"Parameterized complexity","score":0.8817589282989502},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.8259064555168152},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6804988384246826},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6402106881141663},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6326326131820679},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5458846092224121},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49515262246131897},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4890766739845276},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47967052459716797},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.46390482783317566},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.46070778369903564},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4463358521461487},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25276124477386475},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.2288503646850586},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16052493453025818},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.06653600931167603}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.8817589282989502},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.8259064555168152},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6804988384246826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6402106881141663},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6326326131820679},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5458846092224121},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49515262246131897},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4890766739845276},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47967052459716797},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.46390482783317566},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.46070778369903564},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4463358521461487},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25276124477386475},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.2288503646850586},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16052493453025818},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.06653600931167603},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1007/978-3-662-53174-7_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-53174-7_5","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"doi:10.1007/s00453-017-0358-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-017-0358-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00453-017-0358-5.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"},{"id":"pmid:29937611","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29937611","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":null},{"id":"pmh:oai:arXiv.org:1411.6549","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1411.6549","pdf_url":"https://arxiv.org/pdf/1411.6549","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2125332637","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1411.6549.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.763.3879","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.763.3879","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1411.6549.pdf","raw_type":"text"},{"id":"pmh:oai:europepmc.org:4961820","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5976766","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"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":null,"raw_type":"Text"},{"id":"doi:10.48550/arxiv.1411.6549","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1411.6549","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00453-017-0358-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-017-0358-5","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00453-017-0358-5.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/G3027086335","display_name":null,"funder_award_id":"P25607 and Y698","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3631465123","display_name":null,"funder_award_id":"P25607","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7623515682","display_name":null,"funder_award_id":"Y698","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2125332637.pdf","grobid_xml":"https://content.openalex.org/works/W2125332637.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1500603002","https://openalex.org/W1517036688","https://openalex.org/W1570425181","https://openalex.org/W1804601140","https://openalex.org/W1976167318","https://openalex.org/W1989556004","https://openalex.org/W2002722727","https://openalex.org/W2003492950","https://openalex.org/W2004444066","https://openalex.org/W2026705714","https://openalex.org/W2028357390","https://openalex.org/W2059372025","https://openalex.org/W2075024586","https://openalex.org/W2085550081","https://openalex.org/W2091138122","https://openalex.org/W2102931907","https://openalex.org/W2116793595","https://openalex.org/W2132088887","https://openalex.org/W2138118431","https://openalex.org/W2188726364","https://openalex.org/W2411666486","https://openalex.org/W2614441239","https://openalex.org/W2914414140","https://openalex.org/W2914617426","https://openalex.org/W2964156832","https://openalex.org/W2986773320","https://openalex.org/W4213368513","https://openalex.org/W4237683073","https://openalex.org/W4292230561"],"related_works":["https://openalex.org/W2735537192","https://openalex.org/W2183312547","https://openalex.org/W1507115617","https://openalex.org/W3037121613","https://openalex.org/W1792961561","https://openalex.org/W2798325735","https://openalex.org/W2296151834","https://openalex.org/W2953319076","https://openalex.org/W2952352693","https://openalex.org/W2594166360","https://openalex.org/W2263465034","https://openalex.org/W1533622011","https://openalex.org/W3199786338","https://openalex.org/W2092838574","https://openalex.org/W2193891334","https://openalex.org/W1635111306","https://openalex.org/W2623611233","https://openalex.org/W2569746101","https://openalex.org/W2885283474","https://openalex.org/W1790879849"],"abstract_inverted_index":{"A":[0],"secure":[1,42,76,205],"set":[2,11,39,77,203],"<i>S</i>":[3,40],"in":[4,24,43,181,191],"a":[5,10,38,44,67,74,114,188,201],"graph":[6,45,69],"is":[7,33,41,46,52,100,131,140,145,204],"defined":[8],"as":[9,170],"of":[12,22,27,63,80,93,194,208],"vertices":[13,23],"such":[14],"that":[15,35,98,118,128,158],"for":[16,66,78,167,198],"any":[17],"<mml:math":[18,47,101,132,182],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>X</mml:mi><mml:mo>\u2286</mml:mo><mml:mi>S</mml:mi></mml:mrow></mml:math>":[19],"the":[20,25,60,91,105,123,129,143,192],"majority":[21],"neighborhood":[26],"<i>X</i>":[28],"belongs":[29],"to":[30,59,113,147,164],"<i>S</i>.":[31],"It":[32],"known":[34,146],"deciding":[36,64],"whether":[37,65,200],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mtext>co-</mml:mtext><mml:mi>NP</mml:mi></mml:mrow></mml:math>":[48],"-complete.":[49,103],"However,":[50],"it":[51,99],"still":[53],"open":[54],"how":[55],"this":[56,87,94,160],"result":[57,190],"contributes":[58],"actual":[61],"complexity":[62,92,116],"given":[68,202],"<i>G</i>":[70,79],"and":[71,155,185],"integer":[72],"<i>k</i>,":[73],"non-empty":[75],"size":[81,154],"at":[82],"most":[83],"<i>k</i>":[84],"exists.":[85],"In":[86,122],"work,":[88,125],"we":[89,126,173,186],"pinpoint":[90],"problem":[95,106,130,144],"by":[96,137,152,178],"showing":[97,179],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msubsup><mml:mi>\u03a3</mml:mi><mml:mn>2</mml:mn><mml:mi>P</mml:mi></mml:msubsup></mml:math>":[102],"Furthermore,":[104],"has":[107],"so":[108],"far":[109],"not":[110],"been":[111],"subject":[112],"parameterized":[115,136,151],"analysis":[117],"considers":[119],"structural":[120],"parameters.":[121],"present":[124],"prove":[127],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>W</mml:mi><mml:mo>[</mml:mo><mml:mn>1</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:math>":[133],"-hard":[134],"when":[135,150],"treewidth.":[138,210],"This":[139],"surprising":[141],"since":[142],"be":[148,165],"FPT":[149,166,196],"solution":[153],"\"subset":[156],"problems\"":[157],"satisfy":[159],"property":[161],"usually":[162],"tend":[163],"bounded":[168,209],"treewidth":[169],"well.":[171],"Finally,":[172],"give":[174],"an":[175,195],"upper":[176],"bound":[177],"membership":[180],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>XP</mml:mi></mml:math>":[183],",":[184],"provide":[187],"positive":[189],"form":[193],"algorithm":[197],"checking":[199],"on":[206],"graphs":[207]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}