{"id":"https://openalex.org/W3000033813","doi":"https://doi.org/10.1007/s00446-021-00418-2","title":"Equivalence classes and conditional hardness in massively parallel computations","display_name":"Equivalence classes and conditional hardness in massively parallel computations","publication_year":2022,"publication_date":"2022-01-20","ids":{"openalex":"https://openalex.org/W3000033813","doi":"https://doi.org/10.1007/s00446-021-00418-2","mag":"3000033813","pmid":"https://pubmed.ncbi.nlm.nih.gov/35300185"},"language":"en","primary_location":{"id":"doi:10.1007/s00446-021-00418-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00446-021-00418-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00446-021-00418-2.pdf","source":{"id":"https://openalex.org/S139349430","display_name":"Distributed Computing","issn_l":"0178-2770","issn":["0178-2770","1432-0452"],"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":"Distributed Computing","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/s00446-021-00418-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074369690","display_name":"Danupon Nanongkai","orcid":"https://orcid.org/0000-0003-4468-2675"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]},{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["DK","SE"],"is_corresponding":false,"raw_author_name":"Danupon Nanongkai","raw_affiliation_strings":["KTH Royal Institute of Technology, Stockholm, Sweden","University of Copenhagen, Copenhagen, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"University of Copenhagen, Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072734392","display_name":"Michele Scquizzato","orcid":"https://orcid.org/0000-0002-9108-2448"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Michele Scquizzato","raw_affiliation_strings":["University of Padova, Padua, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9108-2448","affiliations":[{"raw_affiliation_string":"University of Padova, Padua, Italy","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5072734392"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":0.9133,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75805038,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"35","issue":"2","first_page":"165","last_page":"183"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/massively-parallel","display_name":"Massively parallel","score":0.7049970626831055},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6921831369400024},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.6453231573104858},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5898538827896118},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4766855239868164},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40484312176704407},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3377690315246582},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.26624736189842224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18742704391479492}],"concepts":[{"id":"https://openalex.org/C190475519","wikidata":"https://www.wikidata.org/wiki/Q544384","display_name":"Massively parallel","level":2,"score":0.7049970626831055},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6921831369400024},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.6453231573104858},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5898538827896118},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4766855239868164},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40484312176704407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3377690315246582},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26624736189842224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18742704391479492}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00446-021-00418-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00446-021-00418-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00446-021-00418-2.pdf","source":{"id":"https://openalex.org/S139349430","display_name":"Distributed Computing","issn_l":"0178-2770","issn":["0178-2770","1432-0452"],"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":"Distributed Computing","raw_type":"journal-article"},{"id":"pmid:35300185","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35300185","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":"Distributed computing","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:8907129","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8907129","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Distrib Comput","raw_type":"Text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/32bc7caf-9280-4678-940e-22b4bdce62b7","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/32bc7caf-9280-4678-940e-22b4bdce62b7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"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":"Nanongkai , D & Scquizzato , M 2022 , ' Equivalence classes and conditional hardness in massively parallel computations ' , Distributed Computing , vol. 35 , no. 2 , pp. 165-183 . https://doi.org/10.1007/s00446-021-00418-2","raw_type":"article"},{"id":"pmh:oai:www.research.unipd.it:11577/3414274","is_oa":true,"landing_page_url":"http://hdl.handle.net/11577/3414274","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00446-021-00418-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00446-021-00418-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00446-021-00418-2.pdf","source":{"id":"https://openalex.org/S139349430","display_name":"Distributed Computing","issn_l":"0178-2770","issn":["0178-2770","1432-0452"],"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":"Distributed Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1836977259","display_name":"Distributed and Dynamic Graph Algorithms and Complexity","funder_award_id":"715672","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4842944547","display_name":null,"funder_award_id":"715672","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G5375430649","display_name":null,"funder_award_id":"BIRD197859/19","funder_id":"https://openalex.org/F4320321966","funder_display_name":"Universit\u00e0 degli Studi di Padova"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321966","display_name":"Universit\u00e0 degli Studi di Padova","ror":"https://ror.org/00240q980"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000033813.pdf","grobid_xml":"https://content.openalex.org/works/W3000033813.grobid-xml"},"referenced_works_count":118,"referenced_works":["https://openalex.org/W1503204712","https://openalex.org/W1503698146","https://openalex.org/W1527197079","https://openalex.org/W1592346261","https://openalex.org/W1598064945","https://openalex.org/W1760158404","https://openalex.org/W1863846876","https://openalex.org/W1945584931","https://openalex.org/W1971680255","https://openalex.org/W1975241280","https://openalex.org/W1980967952","https://openalex.org/W1982129592","https://openalex.org/W1986804393","https://openalex.org/W1987080985","https://openalex.org/W1989887898","https://openalex.org/W1990870868","https://openalex.org/W1991188222","https://openalex.org/W1992996565","https://openalex.org/W1994584977","https://openalex.org/W1994920161","https://openalex.org/W2017205387","https://openalex.org/W2027637765","https://openalex.org/W2028753111","https://openalex.org/W2034616054","https://openalex.org/W2037858972","https://openalex.org/W2038247515","https://openalex.org/W2039302045","https://openalex.org/W2040660972","https://openalex.org/W2045271686","https://openalex.org/W2049516232","https://openalex.org/W2051109346","https://openalex.org/W2051586153","https://openalex.org/W2053061798","https://openalex.org/W2057082426","https://openalex.org/W2071260871","https://openalex.org/W2084867968","https://openalex.org/W2088011174","https://openalex.org/W2100830825","https://openalex.org/W2107805020","https://openalex.org/W2108399535","https://openalex.org/W2110814195","https://openalex.org/W2130305366","https://openalex.org/W2131115830","https://openalex.org/W2153977620","https://openalex.org/W2173213060","https://openalex.org/W2175195593","https://openalex.org/W2177862760","https://openalex.org/W2404196336","https://openalex.org/W2542459869","https://openalex.org/W2545919726","https://openalex.org/W2606089246","https://openalex.org/W2626928698","https://openalex.org/W2734687249","https://openalex.org/W2762968394","https://openalex.org/W2765269579","https://openalex.org/W2767578875","https://openalex.org/W2768882697","https://openalex.org/W2781827254","https://openalex.org/W2788015272","https://openalex.org/W2802632688","https://openalex.org/W2803098354","https://openalex.org/W2807720788","https://openalex.org/W2807926398","https://openalex.org/W2883474934","https://openalex.org/W2884132620","https://openalex.org/W2888820341","https://openalex.org/W2892948282","https://openalex.org/W2898896159","https://openalex.org/W2902509208","https://openalex.org/W2902899861","https://openalex.org/W2936386373","https://openalex.org/W2946823163","https://openalex.org/W2950274216","https://openalex.org/W2951744441","https://openalex.org/W2951940772","https://openalex.org/W2952539154","https://openalex.org/W2962677563","https://openalex.org/W2962710457","https://openalex.org/W2962714610","https://openalex.org/W2963275645","https://openalex.org/W2963298291","https://openalex.org/W2963629655","https://openalex.org/W2963813153","https://openalex.org/W2963974406","https://openalex.org/W2964082996","https://openalex.org/W2964084763","https://openalex.org/W2964104106","https://openalex.org/W2964294252","https://openalex.org/W2971407628","https://openalex.org/W2971736579","https://openalex.org/W2972236337","https://openalex.org/W2972926935","https://openalex.org/W2983623630","https://openalex.org/W2990058971","https://openalex.org/W2995564009","https://openalex.org/W3004078918","https://openalex.org/W3034669632","https://openalex.org/W3040981273","https://openalex.org/W3046888255","https://openalex.org/W3096540095","https://openalex.org/W3098197211","https://openalex.org/W3100301280","https://openalex.org/W3100671347","https://openalex.org/W3101158212","https://openalex.org/W3166172671","https://openalex.org/W3167599539","https://openalex.org/W3183684990","https://openalex.org/W3184913911","https://openalex.org/W4213146104","https://openalex.org/W4230889046","https://openalex.org/W4236835455","https://openalex.org/W4239429564","https://openalex.org/W4240117647","https://openalex.org/W4249997060","https://openalex.org/W4253069973","https://openalex.org/W4298227433","https://openalex.org/W4406653338","https://openalex.org/W6617389157"],"related_works":["https://openalex.org/W2023839151","https://openalex.org/W1774183074","https://openalex.org/W2057488824","https://openalex.org/W2334687145","https://openalex.org/W2178011914","https://openalex.org/W4235962491","https://openalex.org/W2061778832","https://openalex.org/W1513001507","https://openalex.org/W2257153718","https://openalex.org/W3134702077"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Massively":[2],"Parallel":[3],"Computation":[4],"(MPC)":[5],"model":[6,50],"serves":[7],"as":[8,64,259,359,471],"a":[9,130,163,328,368],"common":[10],"abstraction":[11],"of":[12,35,59,133,145,152,159,166,307,331,357,365,450],"many":[13,226,350],"modern":[14],"large-scale":[15],"data":[16],"processing":[17],"frameworks,":[18],"and":[19,143,191,203,211,242,246,304,339,349,458,474],"has":[20],"been":[21],"receiving":[22],"increasingly":[23],"more":[24,116,395],"attention":[25],"over":[26],"the":[27,33,41,57,80,90,119,149,157,169,192,218,232,251,265,277,354,360,382],"past":[28],"few":[29],"years,":[30],"especially":[31],"in":[32,118,162,168,217,231,250],"context":[34],"classical":[36],"graph":[37,65,369],"problems.":[38,134],"So":[39],"far,":[40],"only":[42],"way":[43],"to":[44,52,126,225,311,399,429],"argue":[45],"lower":[46,240,377],"bounds":[47,262,378,463],"for":[48,129,327,445,468],"this":[49,136,425,465],"is":[51,88],"condition":[53],"on":[54,67,94,264],"conjectures":[55,95,213],"about":[56,96],"hardness":[58],"some":[60],"specific":[61],"problems,":[62,333,451],"such":[63,470],"connectivity":[66],"promise":[68],"graphs":[69],"that":[70,121,147,214,220,346],"are":[71,114,215,258,302],"either":[72,306],"one":[73,81,266,371,383],"cycle":[74,82,267,372,384],"or":[75,373],"two":[76,84,269,300,374,386],"cycles,":[77],"usually":[78],"called":[79],"versus":[83,268,385],"cycles":[85,270,387],"problem.":[86],"This":[87],"unlike":[89],"traditional":[91],"arguments":[92],"based":[93],"complexity":[97,195],"classes":[98,144,196],"(e.g.,":[99],"$$\\textsf":[100,174,197,204,278,403],"{P}\\ne":[101],"\\textsf":[102,280,405],"{NP}$$":[103],"<mml:math":[104,177,199,206,283,314,408,432],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[105,178,200,207,284,315,409,433],"<mml:mrow>":[106,179,285,316,410,434],"<mml:mi>P</mml:mi>":[107],"<mml:mo>\u2260</mml:mo>":[108],"<mml:mi>NP</mml:mi>":[109],"</mml:mrow>":[110,188,296,322,421,440],"</mml:math>":[111,189,202,209,297,323,422,441],"),":[112],"which":[113],"often":[115],"robust":[117,216,396],"sense":[120,219],"refuting":[122,221,305],"them":[123,222,308],"would":[124,223,309,427],"lead":[125,224,310,428],"groundbreaking":[127],"algorithms":[128,230,326,444],"whole":[131],"bunch":[132],"In":[135,342],"paper":[137],"we":[138,344],"present":[139],"connections":[140,155],"between":[141,248,367],"problems":[142,146,160,249,348,469],"allow":[148],"latter":[150],"type":[151],"arguments.":[153],"These":[154],"concern":[156],"class":[158],"solvable":[161],"sublogarithmic":[164],"amount":[165],"rounds":[167,358],"MPC":[170,233,252,325,443],"model,":[171],"denoted":[172],"by":[173],"{MPC}(o(\\log":[175,281,406],"N))$$":[176,282,407],"<mml:mi>MPC</mml:mi>":[180,288,413],"<mml:mo>(</mml:mo>":[181,183,289,291,318,414,416,436],"<mml:mi>o</mml:mi>":[182,290,317,415,435],"<mml:mo>log</mml:mo>":[184,292,319,417,437],"<mml:mi>N</mml:mi>":[185,293,320,418,438],"<mml:mo>)</mml:mo>":[186,187,294,295,321,419,420,439],",":[190,210],"standard":[193],"space":[194],"{L}$$":[198],"<mml:mi>L</mml:mi>":[201,286],"{NL}$$":[205],"<mml:mi>NL</mml:mi>":[208,411],"suggest":[212],"surprisingly":[227],"fast":[228],"new":[229,238,244],"model.":[234,253],"We":[235],"also":[236],"obtain":[237],"conditional":[239],"bounds,":[241],"prove":[243],"reductions":[245],"equivalences":[247],"Specifically,":[254],"our":[255],"main":[256],"results":[257],"follows.":[260],"Lower":[261,462],"conditioned":[263],"conjecture":[271,388,426,466],"can":[272,389],"be":[273,390],"instead":[274],"argued":[275,380,391],"under":[276,381,392,464],"{L}\\nsubseteq":[279],"<mml:mo>\u2288</mml:mo>":[287,412],"conjecture:":[298],"these":[299,347],"assumptions":[301],"equivalent,":[303],"$$o(\\log":[312,430],"N)$$":[313,431],"-round":[324,442],"large":[329],"number":[330,356],"challenging":[332],"including":[334,452],"list":[335],"ranking,":[336],"minimum":[337],"cut,":[338],"planarity":[340],"testing.":[341],"fact,":[343],"show":[345],"others":[351],"require":[352],"asymptotically":[353],"same":[355],"seemingly":[361],"much":[362],"easier":[363],"problem":[364],"distinguishing":[366],"being":[370],"cycles.":[375],"Many":[376],"previously":[379],"an":[393,446],"even":[394,447],"(thus":[397],"harder":[398],"refute)":[400],"conjecture,":[401],"namely":[402],"{NL}\\nsubseteq":[404],".":[423],"Refuting":[424],"larger":[448],"set":[449],"all-pairs":[453],"shortest":[454],"paths,":[455],"betweenness":[456],"centrality,":[457],"all":[459],"aforementioned":[460],"ones.":[461],"hold":[467],"perfect":[472],"matching":[473],"network":[475],"flow.":[476]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-23T08:51:43.019350","created_date":"2025-10-10T00:00:00"}