{"id":"https://openalex.org/W2768566391","doi":"https://doi.org/10.1145/3210377.3210409","title":"On the Distributed Complexity of Large-Scale Graph Computations","display_name":"On the Distributed Complexity of Large-Scale Graph Computations","publication_year":2018,"publication_date":"2018-07-11","ids":{"openalex":"https://openalex.org/W2768566391","doi":"https://doi.org/10.1145/3210377.3210409","mag":"2768566391"},"language":"en","primary_location":{"id":"doi:10.1145/3210377.3210409","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3210377.3210409","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3210377.3210409","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3210377.3210409","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089574654","display_name":"Gopal Pandurangan","orcid":"https://orcid.org/0000-0001-5833-6592"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gopal Pandurangan","raw_affiliation_strings":["University of Houston, Cullen Blvd, Houston, TX, USA"],"affiliations":[{"raw_affiliation_string":"University of Houston, Cullen Blvd, Houston, TX, USA","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103150417","display_name":"Peter Robinson","orcid":"https://orcid.org/0000-0002-7442-7002"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Peter Robinson","raw_affiliation_strings":["City University of Hong Kong, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"City University of Hong Kong, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]},{"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":false,"raw_author_name":"Michele Scquizzato","raw_affiliation_strings":["University of Padova, Padova, Italy"],"affiliations":[{"raw_affiliation_string":"University of Padova, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089574654"],"corresponding_institution_ids":["https://openalex.org/I44461941"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00958273,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"8","issue":"2","first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980000257492065,"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/T10237","display_name":"Cryptography and Data Security","score":0.9977999925613403,"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/omega","display_name":"Omega","score":0.6863887310028076},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.608379602432251},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6004734635353088},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.587838888168335},{"id":"https://openalex.org/keywords/pagerank","display_name":"PageRank","score":0.578802764415741},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.5432892441749573},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5185304880142212},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.505760908126831},{"id":"https://openalex.org/keywords/distributed-algorithm","display_name":"Distributed algorithm","score":0.5031699538230896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.441273957490921},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.358273446559906},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.29474759101867676},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23476624488830566}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6863887310028076},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.608379602432251},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6004734635353088},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.587838888168335},{"id":"https://openalex.org/C2779172887","wikidata":"https://www.wikidata.org/wiki/Q184316","display_name":"PageRank","level":2,"score":0.578802764415741},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.5432892441749573},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5185304880142212},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.505760908126831},{"id":"https://openalex.org/C130120984","wikidata":"https://www.wikidata.org/wiki/Q2835898","display_name":"Distributed algorithm","level":2,"score":0.5031699538230896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.441273957490921},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.358273446559906},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.29474759101867676},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23476624488830566},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1145/3210377.3210409","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3210377.3210409","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3210377.3210409","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures","raw_type":"proceedings-article"},{"id":"doi:10.1145/3460900","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3460900","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3460900","source":{"id":"https://openalex.org/S2483380313","display_name":"ACM Transactions on Parallel Computing","issn_l":"2329-4949","issn":["2329-4949","2329-4957"],"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 Parallel Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1602.08481","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.08481","pdf_url":"https://arxiv.org/pdf/1602.08481","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":"","raw_type":"text"},{"id":"mag:2768566391","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1602.08481?context=cs.DS","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":"mag:2804451431","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1602.08481.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:www.research.unipd.it:11577/3290300","is_oa":true,"landing_page_url":"http://hdl.handle.net/11577/3290300","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.48550/arxiv.1602.08481","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1602.08481","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1145/3210377.3210409","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3210377.3210409","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3210377.3210409","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1335521237","display_name":null,"funder_award_id":"Research Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"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/G199314446","display_name":"A Novel Mechanism for Pyrimidine Methylation by a Flavin-dependent Enzyme","funder_award_id":"1213620","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G24500667","display_name":null,"funder_award_id":"CCF-1717075","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3389892740","display_name":"CCF-BSF: AF:Small: Time-Message Tradeoffs in Distributed Algorithms","funder_award_id":"1717075","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3829831297","display_name":"BIGDATA: Collaborative Research: F: Efficient Distributed Computation of Large-Scale Graph Problems in Epidemiology and Contagion Dynamics","funder_award_id":"1633720","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4956428346","display_name":null,"funder_award_id":"Horizon 2020 research and innovatio","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5036817778","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innov","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"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"},{"id":"https://openalex.org/G5399556803","display_name":null,"funder_award_id":"This project has received funding from the Europea","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5514198281","display_name":null,"funder_award_id":"CCF-1540512, IIS-1633720, CCF-1717075","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6111813407","display_name":null,"funder_award_id":"IIS-1633720","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7513945719","display_name":null,"funder_award_id":"CCF-1527867, CCF-1540512, IIS-1633720, and CCF-1717075","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7525902426","display_name":null,"funder_award_id":"CCF-1527867","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7626077044","display_name":null,"funder_award_id":"Project No. 7200639/CS","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8284766523","display_name":null,"funder_award_id":"(NSERC)","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8318064016","display_name":null,"funder_award_id":"Horizon","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G844817646","display_name":null,"funder_award_id":"CCF-1540512","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8482823688","display_name":null,"funder_award_id":"CCF-1527867, CCF-1540512, IIS-1633720, CCF-1717075","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8507846609","display_name":"High-accuracy models in theoretical chemistry","funder_award_id":"200639","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8633428685","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innovat","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8925879480","display_name":"BSF:2014424:Time-Message Tradeoffs in Distributed Algorithms","funder_award_id":"1540512","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/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"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/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2768566391.pdf","grobid_xml":"https://content.openalex.org/works/W2768566391.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W950821216","https://openalex.org/W1518210324","https://openalex.org/W1845051857","https://openalex.org/W1859126261","https://openalex.org/W1945584931","https://openalex.org/W1967022297","https://openalex.org/W1968546622","https://openalex.org/W1971734630","https://openalex.org/W1980744864","https://openalex.org/W1987099434","https://openalex.org/W1992996565","https://openalex.org/W2013414394","https://openalex.org/W2014478203","https://openalex.org/W2015819397","https://openalex.org/W2022994251","https://openalex.org/W2030088585","https://openalex.org/W2040011014","https://openalex.org/W2043522657","https://openalex.org/W2045271686","https://openalex.org/W2051381393","https://openalex.org/W2051586153","https://openalex.org/W2066636486","https://openalex.org/W2083323175","https://openalex.org/W2101014999","https://openalex.org/W2107008873","https://openalex.org/W2107577105","https://openalex.org/W2107805020","https://openalex.org/W2107917944","https://openalex.org/W2107997203","https://openalex.org/W2112090702","https://openalex.org/W2125493559","https://openalex.org/W2129565593","https://openalex.org/W2139535340","https://openalex.org/W2145812340","https://openalex.org/W2161956202","https://openalex.org/W2170616854","https://openalex.org/W2240320246","https://openalex.org/W2255377757","https://openalex.org/W2281539709","https://openalex.org/W2296407087","https://openalex.org/W2460118749","https://openalex.org/W2488670996","https://openalex.org/W2547779378","https://openalex.org/W2570634592","https://openalex.org/W2577167493","https://openalex.org/W2612259229","https://openalex.org/W2618303782","https://openalex.org/W2807720788","https://openalex.org/W2903448613","https://openalex.org/W2950274216","https://openalex.org/W2962708242","https://openalex.org/W2963974406","https://openalex.org/W2964107726","https://openalex.org/W2999961377","https://openalex.org/W3034669632","https://openalex.org/W4205300528","https://openalex.org/W4206219939","https://openalex.org/W4213146104","https://openalex.org/W6674851815","https://openalex.org/W7056210342","https://openalex.org/W7066987989"],"related_works":["https://openalex.org/W2577465605","https://openalex.org/W2007224204","https://openalex.org/W2964030863","https://openalex.org/W2295455748","https://openalex.org/W2964299325","https://openalex.org/W2964175068","https://openalex.org/W2789411239","https://openalex.org/W2963996796","https://openalex.org/W3133121354","https://openalex.org/W2951372599","https://openalex.org/W2962968573","https://openalex.org/W3104625252","https://openalex.org/W2489648777","https://openalex.org/W2028751262","https://openalex.org/W1909439116","https://openalex.org/W2005942657","https://openalex.org/W116139313","https://openalex.org/W2104685510","https://openalex.org/W2022155283","https://openalex.org/W1983365058"],"abstract_inverted_index":{"Motivated":[0],"by":[1,133,168],"the":[2,7,56,70,75,81,87,105,123,127,137,175,203,224,243,272,296,300,334,345,365],"increasing":[3],"need":[4],"to":[5,50,73,99,126,135,153,353],"understand":[6],"distributed":[8,26,109,155,229,289,323,360],"algorithmic":[9],"foundations":[10],"of":[11,77,80,108,130,178,205,223,281,295,298,302,339,367],"large-scale":[12,110],"graph":[13,19,47,181,304,369],"computations,":[14],"we":[15,270],"study":[16],"some":[17],"fundamental":[18,180],"problems":[20,201],"in":[21,62,149,256,305,370],"a":[22,59,93,150,220,237,250,278,288,303,359,368],"message-passing":[23],"model":[24],"for":[25,158,200,231,344],"computing":[27],"where":[28,202,321],"k":[29,57,257],"\u2265":[30],"2":[31,283,307],"machines":[32,134],"jointly":[33],"perform":[34],"computations":[35],"on":[36,104,174],"graphs":[37,317],"with":[38,236,318],"n":[39,42],"nodes":[40,301],"(typically,":[41],">>":[43],"k).":[44],"The":[45],"input":[46],"is":[48,67,72,86,115,141,350],"assumed":[49],"be":[51,97,147],"initially":[52],"randomly":[53],"partitioned":[54],"among":[55],"machines,":[58],"common":[60],"implementation":[61],"many":[63],"real-world":[64],"systems.":[65],"Communication":[66],"point-to-point,":[68],"and":[69,143,186,217,233,286],"goal":[71],"minimize":[74],"number":[76],"communication":[78,206],"rounds":[79,285,343],"computation.":[82],"Our":[83,139],"main":[84],"contribution":[85],"General":[88],"Lower":[89],"Bound":[90],"Theorem":[91],",":[92,258],"theorem":[94,145],"that":[95,121,193,240,253,291,314,362],"can":[96,146,196],"used":[98,148],"show":[100,154,192,271,277,313],"non-trivial":[101,336],"lower":[102,156,172,198,245,279,337],"bounds":[103,157,173,199],"round":[106,124,176,238,251],"complexity":[107,125,177,207,239,252],"data":[111],"computations.":[112],"This":[113,330],"result":[114,331],"established":[116],"via":[117],"an":[118,293],"information-theoretic":[119],"approach":[120,140,195],"relates":[122],"minimal":[128],"amount":[129],"information":[131],"required":[132],"solve":[136],"problem.":[138],"generic,":[142],"this":[144],"\u201ccookbook\u201d":[151],"fashion":[152],"several":[159],"problems,":[160,182],"including":[161,216],"non-graph":[162],"problems.":[163],"We":[164,226,276,312,356],"present":[165,228,287,358],"two":[166,179],"applications":[167,191],"showing":[169],"(almost)":[170,241],"tight":[171,351],"namely,":[183],"PageRank":[184,232,297],"computation":[185],"triangle":[187,234],"enumeration":[188,235],".":[189],"These":[190],"our":[194],"yield":[197],"application":[204],"techniques":[208],"seems":[209],"not":[210],"obvious":[211],"or":[212],"gives":[213],"weak":[214],"bounds,":[215],"especially":[218],"under":[219],"stochastic":[221],"partition":[222],"input.":[225],"then":[227,357],"algorithms":[230,248],"matches":[242],"respective":[244],"bounds;":[246],"these":[247],"exhibit":[249],"scales":[254],"superlinearly":[255],"improving":[259],"significantly":[260],"over":[261],"previous":[262],"results":[263],"[Klauck":[264],"et":[265],"al.,":[266],"SODA":[267],"2015].":[268],"Specifically,":[269],"following":[273],"results:":[274],"PageRank:":[275],"bound":[280,338],"\u1ffa(n/k":[282],")":[284,308,328,342,376],"algorithm":[290,324,361],"computes":[292],"approximation":[294],"all":[299,364],"\u00d5(n/k":[306],"rounds.":[309,329,377],"Triangle":[310],"enumeration:":[311],"there":[315],"exist":[316],"m":[319],"edges":[320],"any":[322],"requires":[325],"\u1ffa(m/k":[326],"5/3":[327,372],"also":[332],"implies":[333],"first":[335],"\u1ffa(n":[340],"1/3":[341],"congested":[346],"clique":[347],"model,":[348],"which":[349],"up":[352],"logarithmic":[354],"factors.":[355],"enumerates":[363],"triangles":[366],"\u00d5(m/k":[371],"+":[373],"n/k":[374],"4/3":[375]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}