{"id":"https://openalex.org/W2556309115","doi":"https://doi.org/10.1145/3576900","title":"On Coalescence Time in Graphs: When Is Coalescing as Fast as Meeting?","display_name":"On Coalescence Time in Graphs: When Is Coalescing as Fast as Meeting?","publication_year":2023,"publication_date":"2023-01-17","ids":{"openalex":"https://openalex.org/W2556309115","doi":"https://doi.org/10.1145/3576900","mag":"2556309115"},"language":"en","primary_location":{"id":"doi:10.1145/3576900","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3576900","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3576900","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3576900","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065655845","display_name":"Varun Kanade","orcid":"https://orcid.org/0000-0002-2300-4819"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210128584","display_name":"The Alan Turing Institute","ror":"https://ror.org/035dkdb55","country_code":"GB","type":"facility","lineage":["https://openalex.org/I4210128584"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Varun Kanade","raw_affiliation_strings":["University of Oxford and The Alan Turing Institute, UK"],"raw_orcid":"https://orcid.org/0000-0002-2300-4819","affiliations":[{"raw_affiliation_string":"University of Oxford and The Alan Turing Institute, UK","institution_ids":["https://openalex.org/I40120149","https://openalex.org/I4210128584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045186573","display_name":"Frederik Mallmann-Trenn","orcid":"https://orcid.org/0000-0003-0363-8547"},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Frederik Mallmann-Trenn","raw_affiliation_strings":["King\u2019s College London, UK","King's College London, UK"],"raw_orcid":"https://orcid.org/0000-0003-0363-8547","affiliations":[{"raw_affiliation_string":"King\u2019s College London, UK","institution_ids":["https://openalex.org/I183935753"]},{"raw_affiliation_string":"King's College London, UK","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017390373","display_name":"Thomas Sauerwald","orcid":"https://orcid.org/0000-0002-0882-283X"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Thomas Sauerwald","raw_affiliation_strings":["University of Cambridge, UK"],"raw_orcid":"https://orcid.org/0000-0002-0882-283X","affiliations":[{"raw_affiliation_string":"University of Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9264,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.72934871,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"2","first_page":"1","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10772","display_name":"Distributed systems and fault tolerance","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T10772","display_name":"Distributed systems and fault tolerance","score":0.9987999796867371,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9976999759674072,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6843128204345703},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.6751411557197571},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6420789957046509},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.617511510848999},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.5881009101867676},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.50289386510849},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4463097155094147},{"id":"https://openalex.org/keywords/coalescence","display_name":"Coalescence (physics)","score":0.4414274990558624},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3371877670288086},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10423943400382996},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09069260954856873}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6843128204345703},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.6751411557197571},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6420789957046509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.617511510848999},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.5881009101867676},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.50289386510849},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4463097155094147},{"id":"https://openalex.org/C149792144","wikidata":"https://www.wikidata.org/wiki/Q2071902","display_name":"Coalescence (physics)","level":2,"score":0.4414274990558624},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3371877670288086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10423943400382996},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09069260954856873},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C87355193","wikidata":"https://www.wikidata.org/wiki/Q411","display_name":"Astrobiology","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1145/3576900","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3576900","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3576900","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:0c47a2d5-7154-4bf8-8f88-a8a454b55b91","is_oa":true,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:0c47a2d5-7154-4bf8-8f88-a8a454b55b91","pdf_url":"https://ora.ox.ac.uk/objects/uuid:0c47a2d5-7154-4bf8-8f88-a8a454b55b91","source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference item"},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/290098","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/290098","pdf_url":"https://www.repository.cam.ac.uk/handle/1810/290098","source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference Object"},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/349444","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/349444","pdf_url":"https://www.repository.cam.ac.uk/bitstreams/8482b099-414a-48ac-8475-a72178512e28/download","source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/1da84feb-c6e8-44b2-973a-da97390dec18","is_oa":false,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/1da84feb-c6e8-44b2-973a-da97390dec18","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"contributionToPeriodical"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:6ec9e434-5136-4974-974b-8d6619a52882","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:6ec9e434-5136-4974-974b-8d6619a52882","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},{"id":"doi:10.17863/cam.37322","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.37322","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Other"}],"best_oa_location":{"id":"doi:10.1145/3576900","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3576900","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3576900","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1309768829","display_name":null,"funder_award_id":"EP/N510129/1.","funder_id":"https://openalex.org/F4320313467","funder_display_name":"Alan Turing Institute"},{"id":"https://openalex.org/G1513559549","display_name":null,"funder_award_id":"CCF0-939370","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1633672591","display_name":null,"funder_award_id":"N510129","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3855435662","display_name":null,"funder_award_id":"N510129","funder_id":"https://openalex.org/F4320313467","funder_display_name":"Alan Turing Institute"},{"id":"https://openalex.org/G444630160","display_name":null,"funder_award_id":"EP/N510129/","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4484632653","display_name":null,"funder_award_id":"EP/W005573/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4500485203","display_name":"The Alan Turing Institute","funder_award_id":"EP/N510129/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5932407296","display_name":"AF: Medium: Distributed Algorithms for Resource-Constrained and Dynamic Settings","funder_award_id":"1461559","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6244900323","display_name":"Emerging Frontiers of Science of Information","funder_award_id":"0939370","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6765781992","display_name":"Using Robust Graph Clustering to Detect Fake News","funder_award_id":"EP/W005573/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8642225238","display_name":"NSF-BSF: AF: Small: An Algorithmic Theory of Brain Networks","funder_award_id":"1810758","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309966","display_name":"\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/05a0dhs15"},{"id":"https://openalex.org/F4320313467","display_name":"Alan Turing Institute","ror":"https://ror.org/035dkdb55"},{"id":"https://openalex.org/F4320322551","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2556309115.pdf","grobid_xml":"https://content.openalex.org/works/W2556309115.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W283401411","https://openalex.org/W1514107797","https://openalex.org/W1578099820","https://openalex.org/W1586184796","https://openalex.org/W1600293573","https://openalex.org/W1676511350","https://openalex.org/W1949110650","https://openalex.org/W1964535518","https://openalex.org/W1985380836","https://openalex.org/W1989183425","https://openalex.org/W1993614623","https://openalex.org/W1994392346","https://openalex.org/W2009169450","https://openalex.org/W2034229945","https://openalex.org/W2039765418","https://openalex.org/W2046265261","https://openalex.org/W2046919262","https://openalex.org/W2049587783","https://openalex.org/W2059959102","https://openalex.org/W2066862787","https://openalex.org/W2095087473","https://openalex.org/W2095530310","https://openalex.org/W2109286989","https://openalex.org/W2109448247","https://openalex.org/W2110742462","https://openalex.org/W2116053806","https://openalex.org/W2142274773","https://openalex.org/W2142465565","https://openalex.org/W2154584815","https://openalex.org/W2156184725","https://openalex.org/W2162775152","https://openalex.org/W2167167562","https://openalex.org/W2198935850","https://openalex.org/W2237112965","https://openalex.org/W2275329125","https://openalex.org/W2294792789","https://openalex.org/W2404093917","https://openalex.org/W2471517265","https://openalex.org/W2533034710","https://openalex.org/W2589531210","https://openalex.org/W2615415387","https://openalex.org/W2621081140","https://openalex.org/W2770485470","https://openalex.org/W2882978176","https://openalex.org/W2907355031","https://openalex.org/W2949361955","https://openalex.org/W2949988259","https://openalex.org/W2952997697","https://openalex.org/W2962742362","https://openalex.org/W2962818201","https://openalex.org/W2963594409","https://openalex.org/W3025584212","https://openalex.org/W3041259449","https://openalex.org/W3103640397","https://openalex.org/W6646488517","https://openalex.org/W6662094196","https://openalex.org/W6713528788","https://openalex.org/W6737417967"],"related_works":["https://openalex.org/W4286907761","https://openalex.org/W2916710807","https://openalex.org/W2413588304","https://openalex.org/W3205447645","https://openalex.org/W2009411567","https://openalex.org/W2371629703","https://openalex.org/W2097769911","https://openalex.org/W2774705104","https://openalex.org/W72835634","https://openalex.org/W2122785676"],"abstract_inverted_index":{"Coalescing":[0],"random":[1,16,39,122,166],"walks":[2,17,123,167],"is":[3,44,112,146,179,192],"a":[4,9,29,37,94,135,185,203,231],"fundamental":[5],"distributed":[6],"process,":[7],"where":[8],"set":[10],"of":[11,68,156,164,184,211,241],"particles":[12,26],"perform":[13],"independent":[14],"discrete-time":[15],"on":[18,223,234],"an":[19],"undirected":[20],"graph.":[21],"Whenever":[22],"two":[23,121],"or":[24],"more":[25,86],"meet":[27],"at":[28,59,126,130],"given":[30],"node,":[31],"they":[32],"merge":[33],"and":[34,238,245,251,259],"continue":[35],"as":[36,46,66,78,114,253,255],"single":[38],"walk.":[40],"The":[41,109],"coalescence":[42,73,162,209],"time":[43,49,74,111,118,145,153,163,171,210,237,240],"defined":[45,113],"the":[47,72,106,115,127,131,151,161,169,182,193,208,224,235],"expected":[48,117],"until":[50],"only":[51,147],"one":[52,57],"particle":[53,58],"remains,":[54],"starting":[55],"from":[56],"every":[60],"node.":[61],"Despite":[62],"recent":[63],"progress":[64],"such":[65,77],"that":[67,97,140,189],"Cooper":[69],"et":[70],"al.,":[71],"for":[75,102,120,141,207],"graphs,":[76,89,243],"binary":[79],"trees,":[80],"d":[81],"-dimensional":[82],"tori,":[83],"hypercubes,":[84],"and,":[85],"generally,":[87],"vertex-transitive":[88],"remains":[90],"unresolved.":[91],"We":[92],"provide":[93],"powerful":[95],"toolkit":[96],"results":[98,219,248],"in":[99],"tight":[100,204],"bounds":[101,222],"various":[103],"topologies":[104],"including":[105],"aforementioned":[107],"ones.":[108],"meeting":[110,144,170],"worst-case":[116,205],"required":[119],"to":[124,173,197],"arrive":[125],"same":[128,132],"node":[129],"time.":[133],"As":[134],"general":[136],"result,":[137],"we":[138,201],"establish":[139],"graphs":[142],"whose":[143],"marginally":[148],"larger":[149],"than":[150],"mixing":[152],"(a":[154],"factor":[155],"log":[157],"2":[158],"n":[159,165],"),":[160],"equals":[168],"up":[172,196],"constant":[174,198],"factors.":[175,199],"This":[176],"upper":[177],"bound":[178,206,233],"complemented":[180],"by":[181,249,257],"construction":[183],"graph":[186],"family":[187],"demonstrating":[188],"this":[190],"result":[191],"best":[194],"possible":[195],"Finally,":[200],"prove":[202],"O(n":[212],"3":[213],")":[214],".":[215],"By":[216],"duality,":[217],"our":[218],"yield":[220,230],"identical":[221],"voter":[225],"model.":[226],"Our":[227],"techniques":[228],"also":[229],"new":[232],"hitting":[236],"cover":[239],"regular":[242],"improving":[244],"tightening":[246],"previous":[247],"Broder":[250],"Karlin,":[252],"well":[254],"those":[256],"Aldous":[258],"Fill.":[260]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}