{"id":"https://openalex.org/W2127076644","doi":"https://doi.org/10.1137/080742166","title":"Querying Approximate Shortest Paths in Anisotropic Regions","display_name":"Querying Approximate Shortest Paths in Anisotropic Regions","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2127076644","doi":"https://doi.org/10.1137/080742166","mag":"2127076644"},"language":"en","primary_location":{"id":"doi:10.1137/080742166","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080742166","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5070497738","display_name":"Siu-Wing Cheng","orcid":"https://orcid.org/0000-0002-3557-9935"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Siu-Wing Cheng","raw_affiliation_strings":["HKUST - Hong Kong University of Science and Technology (Clear Water Bay Kowloon Hong Kong - Hong Kong SAR China)"],"affiliations":[{"raw_affiliation_string":"HKUST - Hong Kong University of Science and Technology (Clear Water Bay Kowloon Hong Kong - Hong Kong SAR China)","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059099525","display_name":"Hyeon-Suk Na","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hyeon-Suk Na","raw_affiliation_strings":["Soongsil University (France)"],"affiliations":[{"raw_affiliation_string":"Soongsil University (France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019937157","display_name":"Antoine Vigneron","orcid":"https://orcid.org/0000-0003-3586-3431"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Antoine Vigneron","raw_affiliation_strings":["MIA-JOUY - Unit\u00e9 de biom\u00e9trie et intelligence artificielle de Jouy (78352 Jouy-en-Josas - France)"],"affiliations":[{"raw_affiliation_string":"MIA-JOUY - Unit\u00e9 de biom\u00e9trie et intelligence artificielle de Jouy (78352 Jouy-en-Josas - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100454881","display_name":"Yajun Wang","orcid":"https://orcid.org/0000-0002-0165-0561"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I4210113369","display_name":"Microsoft Research Asia (China)","ror":"https://ror.org/0300m5276","country_code":"CN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210113369"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Yajun Wang","raw_affiliation_strings":["HKUST - Hong Kong University of Science and Technology (Clear Water Bay Kowloon Hong Kong - Hong Kong SAR China)","Microsoft Research Asia (China)"],"affiliations":[{"raw_affiliation_string":"HKUST - Hong Kong University of Science and Technology (Clear Water Bay Kowloon Hong Kong - Hong Kong SAR China)","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"Microsoft Research Asia (China)","institution_ids":["https://openalex.org/I4210113369"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5070497738"],"corresponding_institution_ids":["https://openalex.org/I200769079"],"apc_list":null,"apc_paid":null,"fwci":2.1628,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.89264766,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"39","issue":"5","first_page":"1888","last_page":"1918"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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/T11106","display_name":"Data Management and Algorithms","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/combinatorics","display_name":"Combinatorics","score":0.7773929834365845},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6153271198272705},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.5916663408279419},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.5607675909996033},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.515308141708374},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5062059760093689},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4907125234603882},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.4852876365184784},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4725477397441864},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.4582400321960449},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4305349886417389},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41127341985702515},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4108425974845886},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19080734252929688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09865525364875793}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7773929834365845},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6153271198272705},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.5916663408279419},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.5607675909996033},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.515308141708374},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5062059760093689},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4907125234603882},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.4852876365184784},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4725477397441864},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.4582400321960449},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4305349886417389},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41127341985702515},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4108425974845886},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19080734252929688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09865525364875793},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"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/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/080742166","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080742166","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02668390v1","is_oa":false,"landing_page_url":"https://hal.inrae.fr/hal-02668390","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Computing, 2010, 39 (5), pp.1888-1918. ⟨10.1137/080742166⟩","raw_type":"Journal articles"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-6556","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-6556","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Article"},{"id":"pmh:oai:scholarworks.unist.ac.kr:201301/19641","is_oa":false,"landing_page_url":"http://epubs.siam.org/doi/abs/10.1137/080742166","pdf_url":null,"source":{"id":"https://openalex.org/S4306401118","display_name":"Scholarworks@UNIST (Ulsan National Institute of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I48566637","host_organization_name":"Ulsan National Institute of Science and Technology","host_organization_lineage":["https://openalex.org/I48566637"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"ARTICLE"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W40061580","https://openalex.org/W1507556857","https://openalex.org/W1559701472","https://openalex.org/W1583421438","https://openalex.org/W1989723858","https://openalex.org/W1996942467","https://openalex.org/W2000744043","https://openalex.org/W2009017109","https://openalex.org/W2018164813","https://openalex.org/W2025130628","https://openalex.org/W2028769163","https://openalex.org/W2031247977","https://openalex.org/W2037134555","https://openalex.org/W2043285556","https://openalex.org/W2049480565","https://openalex.org/W2058510050","https://openalex.org/W2063071084","https://openalex.org/W2112346596","https://openalex.org/W2149906774","https://openalex.org/W3136732126","https://openalex.org/W4248484045"],"related_works":["https://openalex.org/W2384806462","https://openalex.org/W4389950792","https://openalex.org/W2375549870","https://openalex.org/W4376632515","https://openalex.org/W2140072033","https://openalex.org/W2163269603","https://openalex.org/W4205312897","https://openalex.org/W1106115901","https://openalex.org/W2055560755","https://openalex.org/W2386836336"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,12,16,22,35,47,54,89,102,110],"data":[3,86,128],"structure":[4,87,129],"for":[5,68],"answering":[6],"approximate":[7],"shortest":[8,94,112],"path":[9,95,113],"queries":[10],"in":[11,26,46,105,117,138,154],"planar":[13],"subdivision":[14,31,166],"from":[15,97],"fixed":[17,99],"source.":[18],"Let":[19,75],"$\\rho\\geqslant1$":[20],"be":[21,66,77,115,136],"real":[23],"number.":[24],"Distances":[25],"each":[27],"face":[28],"of":[29,92,124,164],"this":[30],"are":[32,73],"measured":[33],"by":[34],"possibly":[36],"asymmetric":[37],"convex":[38,62],"distance":[39,63],"function":[40],"whose":[41],"unit":[42,49],"disk":[43,51,57],"is":[44],"contained":[45],"concentric":[48,55],"Euclidean":[50,56],"and":[52,71,83,134,144],"contains":[53],"with":[58],"radius":[59],"$1/\\rho$.":[60],"Different":[61],"functions":[64],"may":[65],"used":[67],"different":[69],"faces,":[70],"obstacles":[72],"allowed.":[74],"$\\varepsilon$":[76],"any":[78,151,161],"number":[79],"strictly":[80],"between":[81],"0":[82],"1.":[84],"Our":[85,142],"returns":[88],"$(1+\\varepsilon)$":[90],"approximation":[91],"the":[93,98,122,125,165,169],"cost":[96],"source":[100],"to":[101],"query":[103],"destination":[104],"$O(\\log\\frac{\\rho":[106],"n}{\\varepsilon})$":[107,132],"time.":[108,141],"Afterwards,":[109],"$(1+\\varepsilon)$-approximate":[111],"can":[114,135],"reported":[116],"$O(\\log":[118],"n)$":[119],"time":[120,143],"plus":[121],"complexity":[123],"path.":[126],"The":[127],"uses":[130],"$O(\\frac{\\rho^2n^3}{\\varepsilon^2}\\log\\frac{\\rho":[131],"space":[133,145],"built":[137],"$O(\\frac{\\rho^2n^3}{\\varepsilon^2}(\\log\\frac{\\rho":[139],"n}{\\varepsilon})^2)$":[140],"bounds":[146],"do":[147,157],"not":[148,158],"depend":[149,159],"on":[150,160],"other":[152],"parameter;":[153],"particular,":[155],"they":[156],"geometric":[162],"parameter":[163],"such":[167],"as":[168],"minimum":[170],"angle.":[171]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-19T08:26:33.389920","created_date":"2025-10-10T00:00:00"}