{"id":"https://openalex.org/W2962883236","doi":"https://doi.org/10.48550/arxiv.1311.4859","title":"Nucleation-free $3D$ rigidity","display_name":"Nucleation-free $3D$ rigidity","publication_year":2013,"publication_date":"2013-11-19","ids":{"openalex":"https://openalex.org/W2962883236","doi":"https://doi.org/10.48550/arxiv.1311.4859","mag":"2962883236"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1311.4859","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.4859","pdf_url":"https://arxiv.org/pdf/1311.4859","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1311.4859","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114172513","display_name":"Jialong Cheng","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng, Jialong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089647969","display_name":"Meera Sitharam","orcid":"https://orcid.org/0000-0003-1031-1403","observed_orcids":["https://orcid.org/0000-0003-1031-1403"]},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sitharam, Meera","raw_affiliation_strings":["University of Florida, Gainesville, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida, Gainesville, United States","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008565320","display_name":"Ileana Streinu","orcid":"https://orcid.org/0000-0003-2663-2615","observed_orcids":["https://orcid.org/0000-0003-2663-2615"]},"institutions":[{"id":"https://openalex.org/I29867402","display_name":"Central Washington University","ror":"https://ror.org/049c8eh51","country_code":"US","type":"education","lineage":["https://openalex.org/I29867402"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Streinu, Ileana","raw_affiliation_strings":["Central Washington University, Ellensburg, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Central Washington University, Ellensburg, United States","institution_ids":["https://openalex.org/I29867402"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"71","last_page":"74"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.5503000020980835,"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":0.5503000020980835,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.12809999287128448,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11870","display_name":"Structural Analysis and Optimization","score":0.0869000032544136,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bar-and-joint-frameworks","display_name":"bar-joint frameworks","score":0.925000011920929},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.9179999828338623}],"concepts":[{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.7242551445960999},{"id":"https://openalex.org/C61048295","wikidata":"https://www.wikidata.org/wiki/Q909022","display_name":"Nucleation","level":2,"score":0.6618780493736267},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4975273907184601},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4868716299533844},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45083367824554443},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35262250900268555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31932076811790466},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2049884796142578},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10664474964141846},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08459725975990295},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:arXiv.org:1311.4859","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.4859","pdf_url":"https://arxiv.org/pdf/1311.4859","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"pmh:oai:scholarworks.smith.edu:csc_facpubs-1005","doi":null,"is_oa":true,"landing_page_url":"https://scholarworks.smith.edu/csc_facpubs/6","pdf_url":"https://scholarworks.smith.edu/csc_facpubs/6","source":{"id":"https://openalex.org/S4377196392","display_name":"Smith ScholarWorks (Smith College)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I202524275","host_organization_name":"Smith College","host_organization_lineage":["https://openalex.org/I202524275"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computer Science: Faculty Publications","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.174.2096","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.174.2096","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cccg.ca/proceedings/2009/cccg09_19.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.765.3521","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.765.3521","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/1311.4859.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1311.4859","doi":"https://doi.org/10.48550/arxiv.1311.4859","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1311.4859","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"mag:2962883236","doi":null,"is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/corr/corr1311.html#ChengSS13","pdf_url":null,"source":{"id":"https://openalex.org/S4306417878","display_name":"Canadian Conference on Computational Geometry","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Canadian Conference on Computational Geometry","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1311.4859","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.4859","pdf_url":"https://arxiv.org/pdf/1311.4859","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3953922089","display_name":"Multiscale  Macromolecular Assembly Pathways  via  Algebraic  Combinatorics","funder_award_id":"0714912","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G464747895","display_name":"Rigidity, Flexibility, Stress and Motion: Foundations of Reconfiguration Problems in Computational Geometry","funder_award_id":"0728783","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5729303398","display_name":null,"funder_award_id":"CCF-0728783","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G5869185108","display_name":"EMT: Quantum Complementarity and its Algorithmic Implications","funder_award_id":"0622106","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/F4320310638","display_name":"McGill University","ror":"https://ror.org/01pxwe438"},{"id":"https://openalex.org/F4320332169","display_name":"Directorate for Computer and Information Science and Engineering","ror":"https://ror.org/025kzpk63"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1515335033","https://openalex.org/W1528267390","https://openalex.org/W1604628950","https://openalex.org/W1691290619","https://openalex.org/W1980120856","https://openalex.org/W1993907770","https://openalex.org/W2001175168","https://openalex.org/W2008836215","https://openalex.org/W2010786313","https://openalex.org/W2060579930","https://openalex.org/W2062020888","https://openalex.org/W2064178031","https://openalex.org/W2068418846","https://openalex.org/W2069308938","https://openalex.org/W2072645091","https://openalex.org/W2088062469","https://openalex.org/W2106989814","https://openalex.org/W2126314964","https://openalex.org/W2139834426","https://openalex.org/W2526400124"],"related_works":["https://openalex.org/W7125894753","https://openalex.org/W2243956891","https://openalex.org/W3039395340","https://openalex.org/W4226356829","https://openalex.org/W7096256324","https://openalex.org/W2023311234","https://openalex.org/W3038075884","https://openalex.org/W2104960640","https://openalex.org/W7096238643","https://openalex.org/W2137303025"],"abstract_inverted_index":{"When":[0],"all":[1],"non-edge":[2],"distances":[3],"of":[4],"a":[5,11,103,140,164],"graph":[6,25],"realized":[7],"in":[8,32,110,128,171,181],"$\\mathbb{R}^{d}$":[9],"as":[10],"{\\em":[12,17,30,43,69,91,120],"bar-and-joint":[13],"framework}":[14],"are":[15,179],"generically":[16],"implied}":[18],"by":[19,146],"the":[20,24],"bar":[21],"(edge)":[22],"lengths,":[23],"is":[26,55,136],"said":[27],"to":[28,56,73,89,143,183],"be":[29],"rigid}":[31],"$\\mathbb{R}^{d}$.":[33],"For":[34],"$d=3$,":[35],"characterizing":[36],"rigid":[37,65],"graphs,":[38],"determining":[39],"implied":[40,59,100],"non-edges":[41,60],"and":[42,71,86,116,148],"dependent}":[44],"edge":[45,126],"sets":[46,127],"remains":[47],"an":[48,153,158],"elusive,":[49],"long-standing":[50],"open":[51],"problem.":[52],"One":[53],"obstacle":[54],"determine":[57],"when":[58],"can":[61],"exist":[62],"without":[63,96],"non-trivial":[64],"induced":[66],"subgraphs,":[67],"i.e.,":[68,123],"nucleations},":[70],"how":[72],"deal":[74],"with":[75,99],"them.":[76],"In":[77],"this":[78],"paper,":[79],"we":[80,105,162],"give":[81],"general":[82],"inductive":[83,154,166,177],"construction":[84,167],"schemes":[85],"proof":[87],"techniques":[88],"generate":[90],"nucleation-free":[92,119],"graphs}":[93],"(i.e.,":[94],"graphs":[95,109,170],"any":[97],"nucleation)":[98],"non-edges.":[101],"As":[102,157],"consequence,":[104],"obtain":[106,163],"(a)":[107],"dependent":[108,125],"$3D$":[111,118],"that":[112,133],"have":[113],"no":[114],"nucleation;":[115],"(b)":[117],"rigidity":[121,135,144],"circuits},":[122],"minimally":[124],"$d=3$.":[129],"It":[130],"additionally":[131],"follows":[132],"true":[134],"strictly":[137],"stronger":[138],"than":[139],"tractable":[141],"approximation":[142],"given":[145],"Sitharam":[147],"Zhou":[149],"\\cite{sitharam:zhou:tractableADG:2004},":[150],"based":[151],"on":[152],"combinatorial":[155],"characterization.":[156],"independently":[159],"interesting":[160],"byproduct,":[161],"new":[165],"for":[168],"independent":[169],"$3D$.":[172],"Currently,":[173],"very":[174],"few":[175],"such":[176],"constructions":[178],"known,":[180],"contrast":[182],"$2D$.":[184]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2019-07-30T00:00:00"}
