{"id":"https://openalex.org/W2021487870","doi":null,"title":"Geodesic Delaunay triangulation and witness complex in the plane","display_name":"Geodesic Delaunay triangulation and witness complex in the plane","publication_year":2008,"publication_date":"2008-01-20","ids":{"openalex":"https://openalex.org/W2021487870","mag":"2021487870"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.115.3005","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.3005","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.sunysb.edu/~jgao/paper/geodesic_Delaunay.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5037226596","display_name":"Jie Gao","orcid":"https://orcid.org/0000-0001-5083-6082","observed_orcids":["https://orcid.org/0000-0001-5083-6082","https://orcid.org/0000-0001-6095-2968","https://orcid.org/0000-0003-0772-4530"]},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jie Gao","raw_affiliation_strings":["Stony Brook University,Stony Brook,NY"],"raw_orcid":"https://orcid.org/0000-0001-5083-6082","affiliations":[{"raw_affiliation_string":"Stony Brook University,Stony Brook,NY","institution_ids":["https://openalex.org/I59553526"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111954013","display_name":"Leonidas J. Guibas","orcid":"https://orcid.org/0000-0002-8315-4886","observed_orcids":["https://orcid.org/0000-0002-8315-4886"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leonidas Guibas","raw_affiliation_strings":["Stanford University Stanford CA"],"raw_orcid":"https://orcid.org/0000-0002-8315-4886","affiliations":[{"raw_affiliation_string":"Stanford University Stanford CA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032839569","display_name":"Steve Oudot","orcid":"https://orcid.org/0000-0003-2939-9417","observed_orcids":["https://orcid.org/0000-0003-2939-9417"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steve Oudot","raw_affiliation_strings":["Stanford University Stanford CA"],"raw_orcid":"https://orcid.org/0000-0003-2939-9417","affiliations":[{"raw_affiliation_string":"Stanford University Stanford CA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100371981","display_name":"Yue Wang","orcid":"https://orcid.org/0000-0001-9882-3926","observed_orcids":["https://orcid.org/0000-0001-9882-3926"]},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yue Wang","raw_affiliation_strings":["Stony Brook University,Stony Brook,NY"],"raw_orcid":"https://orcid.org/0000-0001-9882-3926","affiliations":[{"raw_affiliation_string":"Stony Brook University,Stony Brook,NY","institution_ids":["https://openalex.org/I59553526"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.2093,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.95036791,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"571","last_page":"580"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9990000128746033,"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":0.9990000128746033,"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":0.0003000000142492354,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/intrinsic-metric","display_name":"intrinsic metric","score":0.7110000252723694},{"id":"https://openalex.org/keywords/homotopy-equivalence","display_name":"homotopy equivalence","score":0.7039999961853027},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"persistent homology","score":0.8140000104904175},{"id":"https://openalex.org/keywords/homology-computation","display_name":"homology computation","score":0.6840000152587891},{"id":"https://openalex.org/keywords/sampling-conditions","display_name":"sampling conditions","score":0.49000000953674316},{"id":"https://openalex.org/keywords/sensor-networks","display_name":"sensor networks","score":0.8040000200271606},{"id":"https://openalex.org/keywords/planar-domains","display_name":"planar domains","score":0.6819999814033508}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.7229231595993042},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.7098817229270935},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6719865798950195},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.6486456394195557},{"id":"https://openalex.org/C128321387","wikidata":"https://www.wikidata.org/wiki/Q5164356","display_name":"Constrained Delaunay triangulation","level":3,"score":0.5132746696472168},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.49468371272087097},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.42987996339797974},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.42857927083969116},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42206746339797974},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3236403465270996},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23799318075180054},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19129744172096252},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.115.3005","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.3005","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.sunysb.edu/~jgao/paper/geodesic_Delaunay.pdf","raw_type":"text"},{"id":"mag:2021487870","doi":null,"is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/conf/soda/soda2008.html#GaoGOW08","pdf_url":null,"source":{"id":"https://openalex.org/S4306420974","display_name":"Symposium on Discrete Algorithms","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":"Symposium on Discrete Algorithms","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W165595478","https://openalex.org/W749223900","https://openalex.org/W1486210143","https://openalex.org/W1522020530","https://openalex.org/W1557324374","https://openalex.org/W1671098680","https://openalex.org/W1980267728","https://openalex.org/W1988523136","https://openalex.org/W2002053510","https://openalex.org/W2019418611","https://openalex.org/W2020428772","https://openalex.org/W2029041800","https://openalex.org/W2043598638","https://openalex.org/W2046305987","https://openalex.org/W2052627089","https://openalex.org/W2083493892","https://openalex.org/W2084533748","https://openalex.org/W2087841994","https://openalex.org/W2093472053","https://openalex.org/W2093766264","https://openalex.org/W2095755994","https://openalex.org/W2107008611","https://openalex.org/W2124036531","https://openalex.org/W2128878012","https://openalex.org/W2135378328","https://openalex.org/W2140862287","https://openalex.org/W2144044408","https://openalex.org/W2157878484","https://openalex.org/W2163787581","https://openalex.org/W2188287671","https://openalex.org/W2199460564","https://openalex.org/W2569270235","https://openalex.org/W2911463656","https://openalex.org/W3040586665","https://openalex.org/W3043060850","https://openalex.org/W3138791075","https://openalex.org/W3159914786","https://openalex.org/W4241752267"],"related_works":["https://openalex.org/W7095176125","https://openalex.org/W2061212063","https://openalex.org/W2046305987","https://openalex.org/W2164270936","https://openalex.org/W7099911037","https://openalex.org/W2604178725","https://openalex.org/W7095090191","https://openalex.org/W387064946","https://openalex.org/W7100757946","https://openalex.org/W7100465358"],"abstract_inverted_index":{"We":[0,180,207],"introduce":[1],"a":[2,16,21,85,113,137,145,187],"novel":[3],"feature":[4,26,74,77,80],"size":[5,27],"for":[6,34,183],"bounded":[7],"planar":[8],"domains":[9],"endowed":[10],"with":[11,70],"an":[12,55],"intrinsic":[13,56],"metric.":[14],"Given":[15],"point":[17],"x":[18,45],"in":[19,50,68,213],"such":[20],"domain":[22],"X,":[23,67],"the":[24,38,41,63,93,106,130,156,170,200,214],"homotopy":[25,120],"of":[28,40,66,88,95,112,117,150,158,163,190,202,216],"X":[29,118,203],"at":[30],"x,":[31],"or":[32],"hfs(x)":[33,59],"short,":[35],"measures":[36],"half":[37],"length":[39],"shortest":[42],"loop":[43],"through":[44],"that":[46,90,105,155,219],"is":[47,119,127],"not":[48],"null-homotopic":[49],"X.":[51,96,123],"The":[52],"resort":[53],"to":[54,62,84,122],"metric":[57],"makes":[58],"rather":[60],"insensitive":[61],"local":[64],"geometry":[65],"contrast":[69],"its":[71,194],"predecessors":[72],"(local":[73],"size,":[75,78],"weak":[76],"homology":[79,157,172,201],"size).":[81],"This":[82],"leads":[83],"reduced":[86],"number":[87],"samples":[89],"still":[91],"capture":[92],"topology":[94],"Under":[97],"reasonable":[98],"sampling":[99,115],"conditions":[100],"involving":[101],"hfs,":[102,185],"we":[103,153],"show":[104],"geodesic":[107,131,195],"Delaunay":[108,196],"traingulation":[109],"DX":[110,125,159],"(L)":[111,126,135,160,175],"finite":[114],"L":[116],"equivalent":[121],"Moreover,":[124],"sandwiched":[128],"between":[129,173],"witness":[132],"complex":[133],"CWX":[134,174,205],"and":[136,176,198],"relaxed":[138],"version":[139],"CWX,":[140,177],"v":[141,178],"(L),":[142],"defined":[143],"by":[144,168],"parameter":[146],"v.":[147],"Taking":[148],"advantage":[149],"this":[151],"fact,":[152],"prove":[154],"(and":[161],"hence":[162],"X)":[164],"can":[165],"be":[166],"retrieved":[167],"computing":[169,199],"persistent":[171],"(L).":[179,206],"propose":[181],"algorithms":[182],"estimating":[184],"selecting":[186],"landmark":[188],"set":[189],"sufficient":[191],"density,":[192],"building":[193],"triangulation,":[197],"using":[204],"also":[208],"present":[209],"some":[210],"simulation":[211],"results":[212],"context":[215],"sensor":[217],"networks":[218],"corroborate":[220],"our":[221],"theoretical":[222],"statements.":[223]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2016-06-24T00:00:00"}
