{"id":"https://openalex.org/W2086952960","doi":"https://doi.org/10.1145/1998196.1998230","title":"Reeb graphs","display_name":"Reeb graphs","publication_year":2011,"publication_date":"2011-06-13","ids":{"openalex":"https://openalex.org/W2086952960","doi":"https://doi.org/10.1145/1998196.1998230","mag":"2086952960"},"language":"en","primary_location":{"id":"doi:10.1145/1998196.1998230","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1998196.1998230","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-seventh annual symposium on Computational geometry","raw_type":"proceedings-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/A5025354167","display_name":"Tamal K. Dey","orcid":"https://orcid.org/0000-0001-5160-9738"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tamal K. Dey","raw_affiliation_strings":["The Ohio State University, Columbus, OH, USA","The Ohio State University, Columbus, OH, USA.;"],"affiliations":[{"raw_affiliation_string":"The Ohio State University, Columbus, OH, USA","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"The Ohio State University, Columbus, OH, USA.;","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101536052","display_name":"Yusu Wang","orcid":"https://orcid.org/0000-0001-7950-4348"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yusu Wang","raw_affiliation_strings":["The Ohio State University, Columbus, OH, USA","The Ohio State University, Columbus, OH, USA.;"],"affiliations":[{"raw_affiliation_string":"The Ohio State University, Columbus, OH, USA","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"The Ohio State University, Columbus, OH, USA.;","institution_ids":["https://openalex.org/I52357470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025354167"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":3.4522,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.92751513,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"226","last_page":"235"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9656000137329102,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9444000124931335,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6382253170013428},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5551316738128662},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.544853925704956},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4351215064525604},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.41327688097953796},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3546982407569885},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32236558198928833}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6382253170013428},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5551316738128662},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.544853925704956},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4351215064525604},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.41327688097953796},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3546982407569885},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32236558198928833},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1998196.1998230","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1998196.1998230","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-seventh annual symposium on Computational geometry","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W127493627","https://openalex.org/W156852151","https://openalex.org/W582625930","https://openalex.org/W1496383623","https://openalex.org/W1526212284","https://openalex.org/W1976067114","https://openalex.org/W1998382058","https://openalex.org/W2001887552","https://openalex.org/W2003860334","https://openalex.org/W2009940349","https://openalex.org/W2011751494","https://openalex.org/W2024913803","https://openalex.org/W2036865416","https://openalex.org/W2075608792","https://openalex.org/W2089763657","https://openalex.org/W2091452023","https://openalex.org/W2096331512","https://openalex.org/W2097305921","https://openalex.org/W2109354433","https://openalex.org/W2148010629","https://openalex.org/W2157878484","https://openalex.org/W2158407067","https://openalex.org/W2161184224","https://openalex.org/W2198493461","https://openalex.org/W2486762503","https://openalex.org/W2913946465","https://openalex.org/W3013843370","https://openalex.org/W3040586665","https://openalex.org/W3138205514","https://openalex.org/W4233690291","https://openalex.org/W4251358505","https://openalex.org/W6629795034"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4231775656","https://openalex.org/W2980963558","https://openalex.org/W2046435967","https://openalex.org/W2383646825","https://openalex.org/W2371018915","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905"],"abstract_inverted_index":{"Given":[0],"a":[1,8,22,46,97,100,112,122,143,179],"continuous":[2],"function":[3,98],"f:X":[4],"->":[5],"S":[6],"on":[7,51,56,99],"topological":[9],"space":[10],"X,":[11],"its":[12,57,78],"level":[13,30],"set":[14,113],"f-1(a)":[15],"changes":[16],"continuously":[17],"as":[18,134,136],"the":[19,25,29,65,72,90,93,125,129,151,154,169,172,175,198],"real":[20],"value":[21],"changes.":[23],"Consequently,":[24],"connected":[26],"components":[27],"in":[28,81,139,142],"sets":[31],"appear,":[32],"disappear,":[33],"split":[34],"and":[35,83,128,141],"merge.":[36],"The":[37,86,107,205],"Reeb":[38,52,73,94,126,155],"graph":[39,47,53,74,95,127,156],"of":[40,67,71,92,96,114,153,171,174,200],"f":[41],"summarizes":[42],"this":[43,61,211],"information":[44],"into":[45],"structure.":[48],"Previous":[49],"work":[50],"mainly":[54],"focused":[55],"efficient":[58,191],"computation.":[59],"In":[60],"paper,":[62],"we":[63,149,187],"initiate":[64],"study":[66],"two":[68],"important":[69],"aspects":[70],"which":[75],"can":[76],"facilitate":[77],"broader":[79],"applications":[80],"shape":[82],"data":[84],"analysis.":[85],"first":[87],"one":[88],"is":[89,109,168,183],"approximation":[91,108],"smooth":[101],"compact":[102],"manifold":[103],"M":[104,140,182],"without":[105],"boundary.":[106],"computed":[110],"from":[111,118,147,157,202],"points":[115],"P":[116],"sampled":[117],"M.":[119],"By":[120],"leveraging":[121],"relation":[123],"between":[124,137],"so-called":[130],"vertical":[131],"homology":[132],"group,":[133],"well":[135],"cycles":[138],"Rips":[144,176],"complex":[145],"constructed":[146],"P,":[148],"compute":[150,197],"H1-homology":[152],"P.":[158],"It":[159],"takes":[160,213],"O(n":[161],"log":[162],"n)":[163],"expected":[164],"time,":[165],"where":[166],"n":[167],"size":[170],"2-skeleton":[173],"complex.":[177],"As":[178],"by-product,":[180],"when":[181],"an":[184,190],"orientable":[185],"2-manifold,":[186],"also":[188],"obtain":[189],"near-linear":[192],"time":[193,215],"(expected)":[194],"algorithm":[195,209],"to":[196],"rank":[199],"H1(MM)":[201],"point":[203,217],"data.":[204,218],"best":[206],"known":[207],"previous":[208],"for":[210,216],"problem":[212],"O(n3)":[214]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}