{"id":"https://openalex.org/W1553663209","doi":"https://doi.org/10.1007/s00224-014-9558-4","title":"Sitting Closer to Friends than Enemies, Revisited","display_name":"Sitting Closer to Friends than Enemies, Revisited","publication_year":2014,"publication_date":"2014-06-30","ids":{"openalex":"https://openalex.org/W1553663209","doi":"https://doi.org/10.1007/s00224-014-9558-4","mag":"1553663209","pmid":"https://pubmed.ncbi.nlm.nih.gov/26300686"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-014-9558-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-014-9558-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-014-9558-4.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00224-014-9558-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037989463","display_name":"Marek Cygan","orcid":"https://orcid.org/0000-0003-2472-2975"},"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":false,"raw_author_name":"Marek Cygan","raw_affiliation_strings":["Institute of Informatics, University of Warsaw, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059330513","display_name":"Marcin Pilipczuk","orcid":"https://orcid.org/0000-0001-5680-7397"},"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"]},{"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":["NO","PL"],"is_corresponding":false,"raw_author_name":"Marcin Pilipczuk","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway","Institute of Informatics, University of Warsaw, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000479623","display_name":"Micha\u0142 Pilipczuk","orcid":"https://orcid.org/0000-0001-7891-1988"},"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"]},{"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":["NO","PL"],"is_corresponding":true,"raw_author_name":"Marcin Pilipczuk","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway","Institute of Informatics, University of Warsaw, Warsaw, Poland","Department\u00a0of Informatics, University of Bergen, Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Department\u00a0of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083165224","display_name":"Jakub Onufry Wojtaszczyk","orcid":null},"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"]},{"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":["NO","PL"],"is_corresponding":true,"raw_author_name":"Micha\u0142 Pilipczuk","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway","Institute of Informatics, University of Warsaw, Warsaw, Poland","Google Inc., Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Google Inc., Warsaw, Poland","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000479623","display_name":"Micha\u0142 Pilipczuk","orcid":"https://orcid.org/0000-0001-7891-1988"},"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"]},{"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":["NO","PL"],"is_corresponding":false,"raw_author_name":"Micha\u0142 Pilipczuk","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway","Institute of Informatics, University of Warsaw, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083165224","display_name":"Jakub Onufry Wojtaszczyk","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jakub Onufry Wojtaszczyk","raw_affiliation_strings":["Google Inc., Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Inc., Warsaw, Poland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000479623","https://openalex.org/A5083165224"],"corresponding_institution_ids":["https://openalex.org/I4432739","https://openalex.org/I4654613"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.03405485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"56","issue":"2","first_page":"394","last_page":"405"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9976999759674072,"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":0.9958000183105469,"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":0.6953287720680237},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6416412591934204},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6022082567214966},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5195832252502441},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.5187892317771912},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4992399215698242},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4555285573005676},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.454346626996994},{"id":"https://openalex.org/keywords/exponential-time-hypothesis","display_name":"Exponential time hypothesis","score":0.4271785020828247},{"id":"https://openalex.org/keywords/signed-graph","display_name":"Signed graph","score":0.42349737882614136},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41077959537506104}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6953287720680237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6416412591934204},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6022082567214966},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5195832252502441},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.5187892317771912},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4992399215698242},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4555285573005676},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.454346626996994},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.4271785020828247},{"id":"https://openalex.org/C2779773260","wikidata":"https://www.wikidata.org/wiki/Q11246292","display_name":"Signed graph","level":3,"score":0.42349737882614136},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41077959537506104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00224-014-9558-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-014-9558-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-014-9558-4.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmid:26300686","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26300686","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":"Theory of computing systems","raw_type":null},{"id":"pmh:oai:wrap.warwick.ac.uk:66093","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:europepmc.org:3518834","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4540112","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"}],"best_oa_location":{"id":"doi:10.1007/s00224-014-9558-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-014-9558-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-014-9558-4.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6299999952316284}],"awards":[{"id":"https://openalex.org/G2761285720","display_name":null,"funder_award_id":"FP/2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5593277320","display_name":null,"funder_award_id":"2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5803244198","display_name":null,"funder_award_id":"2007-2013","funder_id":"https://openalex.org/F4320321042","funder_display_name":"Fundacja na rzecz Nauki Polskiej"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321042","display_name":"Fundacja na rzecz Nauki Polskiej","ror":"https://ror.org/048zd9m77"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1553663209.pdf","grobid_xml":"https://content.openalex.org/works/W1553663209.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W108936587","https://openalex.org/W1547966581","https://openalex.org/W1580484824","https://openalex.org/W1890176618","https://openalex.org/W1964095725","https://openalex.org/W1985572324","https://openalex.org/W1995725694","https://openalex.org/W2011039300","https://openalex.org/W2014290730","https://openalex.org/W2021111619","https://openalex.org/W2037583329","https://openalex.org/W2059260882","https://openalex.org/W2072701859","https://openalex.org/W2073415627","https://openalex.org/W2086647704","https://openalex.org/W2114051435","https://openalex.org/W2117134415","https://openalex.org/W2138126900","https://openalex.org/W2142517301","https://openalex.org/W2156894402","https://openalex.org/W2233339885","https://openalex.org/W2570842749","https://openalex.org/W2950392007"],"related_works":["https://openalex.org/W4214914101","https://openalex.org/W3196775331","https://openalex.org/W2256089709","https://openalex.org/W4327715695","https://openalex.org/W4287689012","https://openalex.org/W2000333212","https://openalex.org/W4287025685","https://openalex.org/W3049215996","https://openalex.org/W1540768932","https://openalex.org/W2964091527"],"abstract_inverted_index":{"Signed":[0],"graphs,":[1],"i.e.,":[2],"undirected":[3],"graphs":[4,127],"with":[5,8],"edges":[6,189],"labelled":[7],"a":[9,56,89,98,180,203,209],"plus":[10],"or":[11],"minus":[12],"sign,":[13],"are":[14],"commonly":[15],"used":[16],"to":[17,63,72,136],"model":[18],"relationships":[19],"in":[20,54,156,213],"social":[21],"networks.":[22],"Recently,":[23],"Kermarrec":[24,109,118],"and":[25,110,119,163,188],"Thraves":[26,120],"(2011)":[27],"initiated":[28],"the":[29,32,37,49,115,122,131,137,147,167,171,177,184,191,198,214],"study":[30,100],"of":[31,34,101,117,124,139,170,179,186,190,216],"problem":[33,132],"appropriately":[35],"visualising":[36],"network:":[38],"They":[39],"asked":[40],"whether":[41],"any":[42],"signed":[43,126,193],"graph":[44],"can":[45,85],"be":[46,86],"embedded":[47],"into":[48,82],"metric":[50],"space":[51],"${{\\mathbb":[52,83],"{R}}}^{l}$":[53],"such":[55],"manner":[57],"that":[58,130,146,176],"every":[59],"vertex":[60],"is":[61,133,155],"closer":[62],"all":[64,73],"its":[65,74],"friends":[66],"(neighbours":[67,76],"via":[68,77],"positive":[69],"edges)":[70],"than":[71],"enemies":[75],"negative":[78],"edges).":[79],"Interestingly,":[80],"embeddability":[81],"{R}}}^{1}$":[84],"expressed":[87],"as":[88],"purely":[90],"combinatorial":[91],"problem.":[92],"In":[93],"this":[94,102],"paper":[95],"we":[96,113,144,160,174],"pursue":[97],"deeper":[99],"case,":[103,149],"answering":[104],"several":[105],"questions":[106],"posed":[107],"by":[108,128],"Thraves.":[111],"First,":[112],"refine":[114],"approach":[116,207],"for":[121,166],"case":[123],"complete":[125],"showing":[129],"closely":[134],"related":[135],"recognition":[138],"proper":[140],"interval":[141],"graphs.":[142],"Second,":[143],"prove":[145,175],"general":[148,172],"whose":[150],"polynomial-time":[151],"tractability":[152],"remained":[153],"open,":[154],"fact":[157],"NP-complete.":[158],"Finally,":[159],"provide":[161],"lower":[162],"upper":[164],"bounds":[165],"time":[168,182,211],"complexity":[169],"case:":[173],"existence":[178],"subexponential":[181],"(in":[183],"number":[185,215],"vertices":[187],"input":[192],"graph)":[194],"algorithm":[195],"would":[196],"violate":[197],"Exponential":[199],"Time":[200],"Hypothesis,":[201],"whereas":[202],"simple":[204],"dynamic":[205],"programming":[206],"gives":[208],"running":[210],"single-exponential":[212],"vertices.":[217]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4}],"updated_date":"2026-07-18T07:39:51.176621","created_date":"2025-10-10T00:00:00"}
