{"id":"https://openalex.org/W1963737727","doi":"https://doi.org/10.1145/2629613","title":"The Convergence of Bird Flocking","display_name":"The Convergence of Bird Flocking","publication_year":2014,"publication_date":"2014-07-01","ids":{"openalex":"https://openalex.org/W1963737727","doi":"https://doi.org/10.1145/2629613","mag":"1963737727"},"language":"en","primary_location":{"id":"doi:10.1145/2629613","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2629613","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044565966","display_name":"Bernard Chazelle","orcid":"https://orcid.org/0000-0001-8542-0247"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bernard Chazelle","raw_affiliation_strings":["Princeton University","Princeton University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044565966"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":6.229,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.96264306,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"61","issue":"4","first_page":"1","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"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/T12784","display_name":"Modular Robots and Swarm Intelligence","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9782999753952026,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/flocking","display_name":"Flocking (texture)","score":0.9676024913787842},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5069096684455872},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5064984560012817},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4925459325313568},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.45396363735198975},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43842944502830505},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.43676912784576416},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.399260938167572},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33134645223617554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16134527325630188},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1322478950023651}],"concepts":[{"id":"https://openalex.org/C2781220375","wikidata":"https://www.wikidata.org/wiki/Q814208","display_name":"Flocking (texture)","level":2,"score":0.9676024913787842},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5069096684455872},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5064984560012817},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4925459325313568},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.45396363735198975},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43842944502830505},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.43676912784576416},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.399260938167572},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33134645223617554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16134527325630188},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1322478950023651},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2629613","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2629613","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.250.7272","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.7272","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0905.4241v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.644.5525","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.644.5525","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.princeton.edu/~chazelle/pubs/flocking.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G488171630","display_name":null,"funder_award_id":"CCF-0634958, NSF CCF-0832797","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"}],"funders":[{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W1497826971","https://openalex.org/W1506764403","https://openalex.org/W1508718255","https://openalex.org/W1512825212","https://openalex.org/W1516027685","https://openalex.org/W1522727408","https://openalex.org/W1578099820","https://openalex.org/W1614210333","https://openalex.org/W1615818243","https://openalex.org/W1629051378","https://openalex.org/W1964126948","https://openalex.org/W1965412489","https://openalex.org/W1974280710","https://openalex.org/W1983122377","https://openalex.org/W1986434677","https://openalex.org/W1994390718","https://openalex.org/W2001258629","https://openalex.org/W2015410655","https://openalex.org/W2018580609","https://openalex.org/W2019761982","https://openalex.org/W2038358424","https://openalex.org/W2044247492","https://openalex.org/W2047733028","https://openalex.org/W2070842753","https://openalex.org/W2075379212","https://openalex.org/W2093047029","https://openalex.org/W2105850748","https://openalex.org/W2111363006","https://openalex.org/W2112164016","https://openalex.org/W2124351843","https://openalex.org/W2125668987","https://openalex.org/W2128928412","https://openalex.org/W2137216672","https://openalex.org/W2144579655","https://openalex.org/W2150312211","https://openalex.org/W2153081079","https://openalex.org/W2161979183","https://openalex.org/W2165469059","https://openalex.org/W2165744313","https://openalex.org/W2166687004","https://openalex.org/W2169846294","https://openalex.org/W2172813797","https://openalex.org/W2480138299","https://openalex.org/W2489187236","https://openalex.org/W2802074788","https://openalex.org/W2810946555","https://openalex.org/W2963585663","https://openalex.org/W2963999286","https://openalex.org/W2993433457","https://openalex.org/W4234406933","https://openalex.org/W4299581770","https://openalex.org/W6630178116","https://openalex.org/W6630827198","https://openalex.org/W6684411828"],"related_works":["https://openalex.org/W3196562632","https://openalex.org/W2530977643","https://openalex.org/W4318822799","https://openalex.org/W1989157904","https://openalex.org/W3099149755","https://openalex.org/W1481047111","https://openalex.org/W2357545018","https://openalex.org/W2033806705","https://openalex.org/W1589381382","https://openalex.org/W961142965"],"abstract_inverted_index":{"We":[0,31,50],"bound":[1],"the":[2,33,46,52],"time":[3,47],"it":[4],"takes":[5],"for":[6],"a":[7,14,28],"group":[8],"of":[9,36],"birds":[10],"to":[11,48,54],"stabilize":[12],"in":[13,58],"standard":[15],"flocking":[16],"model.":[17],"Each":[18],"bird":[19],"averages":[20],"its":[21,24],"velocity":[22],"with":[23],"neighbors":[25],"lying":[26],"within":[27],"fixed":[29],"radius.":[30],"resolve":[32],"worst-case":[34],"complexity":[35],"this":[37],"natural":[38],"algorithm":[39],"by":[40],"providing":[41],"asymptotically":[42],"tight":[43],"bounds":[44],"on":[45],"equilibrium.":[49],"reduce":[51],"problem":[53],"two":[55],"distinct":[56],"questions":[57],"computational":[59],"geometry":[60],"and":[61],"circuit":[62],"complexity.":[63]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}