{"id":"https://openalex.org/W1963750764","doi":"https://doi.org/10.1137/s0097539703435297","title":"Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time","display_name":"Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1963750764","doi":"https://doi.org/10.1137/s0097539703435297","mag":"1963750764"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539703435297","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539703435297","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/A5051815913","display_name":"Artur Czumaj","orcid":"https://orcid.org/0000-0002-7743-438X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Artur Czumaj","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033348209","display_name":"Funda Erg\u00fcn","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Funda Erg\u00fcn","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075191567","display_name":"Lance Fortnow","orcid":"https://orcid.org/0000-0002-2020-1358"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lance Fortnow","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043150610","display_name":"Avner Magen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Avner Magen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005870042","display_name":"Ilan Newman","orcid":"https://orcid.org/0000-0002-4845-4111"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ilan Newman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041567023","display_name":"Ronitt Rubinfeld","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ronitt Rubinfeld","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034247955","display_name":"Christian Sohler","orcid":"https://orcid.org/0000-0001-8990-3326"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Sohler","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5051815913"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0371,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.91213162,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"35","issue":"1","first_page":"91","last_page":"109"},"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":0.9976000189781189,"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.7655181884765625},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7604203224182129},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.6837975382804871},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.6643306612968445},{"id":"https://openalex.org/keywords/euclidean-minimum-spanning-tree","display_name":"Euclidean minimum spanning tree","score":0.6436086893081665},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6406020522117615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5975658893585205},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.5272173881530762},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.46336764097213745},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46264517307281494},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45467811822891235},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.45129793882369995},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.43269580602645874},{"id":"https://openalex.org/keywords/minimum-bounding-box","display_name":"Minimum bounding box","score":0.41718313097953796},{"id":"https://openalex.org/keywords/minimum-degree-spanning-tree","display_name":"Minimum degree spanning tree","score":0.41510075330734253},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.41290947794914246},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38834843039512634},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2036767303943634}],"concepts":[{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.7655181884765625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7604203224182129},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.6837975382804871},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6643306612968445},{"id":"https://openalex.org/C145685049","wikidata":"https://www.wikidata.org/wiki/Q4454941","display_name":"Euclidean minimum spanning tree","level":4,"score":0.6436086893081665},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6406020522117615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5975658893585205},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.5272173881530762},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.46336764097213745},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46264517307281494},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45467811822891235},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.45129793882369995},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.43269580602645874},{"id":"https://openalex.org/C147037132","wikidata":"https://www.wikidata.org/wiki/Q6865426","display_name":"Minimum bounding box","level":3,"score":0.41718313097953796},{"id":"https://openalex.org/C64271015","wikidata":"https://www.wikidata.org/wiki/Q6865444","display_name":"Minimum degree spanning tree","level":3,"score":0.41510075330734253},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.41290947794914246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38834843039512634},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2036767303943634},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/s0097539703435297","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539703435297","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:CiteSeerX.psu:10.1.1.129.7860","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.129.7860","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.csail.mit.edu/~ronitt/papers/emst.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.6820","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.6820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cis.njit.edu/~czumaj/PUBLICATIONS/MyPublications/SICOMP-Czumaj-Ergun-Fortnow-Magen-Newman-Rubinfeld-Sohler-SICOMP-35-1-2005-91-109.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.58.2190","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.58.2190","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~avner/papers/emst.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.78.6234","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.6234","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.cs.uchicago.edu/~fortnow/papers/emst.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.84.4509","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.84.4509","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.utoronto.ca/~avner/papers/emst-full.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.9.8461","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.9.8461","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.cs.uchicago.edu/~fortnow/papers/./emst.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W108314478","https://openalex.org/W1505388833","https://openalex.org/W1515019821","https://openalex.org/W1526220139","https://openalex.org/W1552092932","https://openalex.org/W2004476837","https://openalex.org/W2007610503","https://openalex.org/W2024833542","https://openalex.org/W2028430839","https://openalex.org/W2031671531","https://openalex.org/W2038521122","https://openalex.org/W2082551413","https://openalex.org/W2085933841","https://openalex.org/W2093120238","https://openalex.org/W2093241092","https://openalex.org/W2118224498","https://openalex.org/W2127366419","https://openalex.org/W2134165468","https://openalex.org/W2136963423","https://openalex.org/W2149906774","https://openalex.org/W2160816205","https://openalex.org/W2611804663","https://openalex.org/W2913207943","https://openalex.org/W3082744303","https://openalex.org/W4214494916","https://openalex.org/W4230573295"],"related_works":["https://openalex.org/W98489388","https://openalex.org/W1601733264","https://openalex.org/W2011697681","https://openalex.org/W2162077219","https://openalex.org/W2116207970","https://openalex.org/W2973878682","https://openalex.org/W2121599632","https://openalex.org/W1963750764","https://openalex.org/W2152434295","https://openalex.org/W2000579002"],"abstract_inverted_index":{"We":[0,23,56],"consider":[1],"the":[2,6,26,29,50,65,97],"problem":[3],"of":[4,8,17,67,73,76],"computing":[5],"weight":[7,66],"a":[9,15,53,68,74,102],"Euclidean":[10,69],"minimum":[11,70],"spanning":[12,71],"tree":[13,72],"for":[14,90],"set":[16,32,75],"n":[18],"points":[19,77],"in":[20,52],"$\\mathbb":[21],"R^d$.":[22],"focus":[24],"on":[25],"setting":[27],"where":[28],"input":[30,51,98],"point":[31],"is":[33,99],"supported":[34,100],"by":[35,101,108,113],"certain":[36],"basic":[37],"(and":[38],"commonly":[39],"used)":[40],"geometric":[41],"data":[42],"structures":[43],"that":[44,60,96],"can":[45],"provide":[46],"efficient":[47],"access":[48],"to":[49,78],"structured":[54],"way.":[55],"present":[57],"an":[58],"algorithm":[59,94],"estimates":[61],"with":[62],"high":[63],"probability":[64],"within":[79],"$1":[80],"+":[81],"\\eps$":[82],"using":[83],"only":[84],"$\\widetilde{\\O}(\\sqrt{n}":[85],"\\,":[86],"\\text{poly}":[87],"(1/\\eps))$":[88],"queries":[89],"constant":[91],"d.":[92],"The":[93],"assumes":[95],"minimal":[103],"bounding":[104],"cube":[105],"enclosing":[106],"it,":[107],"orthogonal":[109],"range":[110],"queries,":[111],"and":[112],"cone":[114],"approximate":[115],"nearest":[116],"neighbor":[117],"queries.":[118]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
