{"id":"https://openalex.org/W2778138247","doi":"https://doi.org/10.20382/jocg.v11i1a21","title":"Time-Space Trade-Offs for Computing Euclidean Minimum Spanning Trees","display_name":"Time-Space Trade-Offs for Computing Euclidean Minimum Spanning Trees","publication_year":2017,"publication_date":"2017-12-18","ids":{"openalex":"https://openalex.org/W2778138247","doi":"https://doi.org/10.20382/jocg.v11i1a21","mag":"2778138247"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1712.06431","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.06431","pdf_url":"https://arxiv.org/pdf/1712.06431","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1712.06431","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040964919","display_name":"Bahareh Banyassady","orcid":"https://orcid.org/0000-0002-3422-9028"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Banyassady, Bahareh","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038157909","display_name":"Luis Barba","orcid":"https://orcid.org/0000-0001-8732-6799"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barba, Luis","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090438334","display_name":"Wolfgang Mulzer","orcid":"https://orcid.org/0000-0002-1948-5840"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mulzer, Wolfgang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040964919"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25169703,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/spanning-tree","display_name":"Spanning tree","score":0.8294128179550171},{"id":"https://openalex.org/keywords/euclidean-minimum-spanning-tree","display_name":"Euclidean minimum spanning tree","score":0.7710875272750854},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.6980384588241577},{"id":"https://openalex.org/keywords/kruskals-algorithm","display_name":"Kruskal's algorithm","score":0.6720007061958313},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5879135131835938},{"id":"https://openalex.org/keywords/workspace","display_name":"Workspace","score":0.5135972499847412},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5132761001586914},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5077358484268188},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4890631139278412},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4833680987358093},{"id":"https://openalex.org/keywords/minimum-degree-spanning-tree","display_name":"Minimum degree spanning tree","score":0.48007112741470337},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.46016380190849304},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4550950229167938},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4432704448699951},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44051510095596313},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.42855381965637207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3799639642238617},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3662082850933075},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12610793113708496},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.08827334642410278}],"concepts":[{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.8294128179550171},{"id":"https://openalex.org/C145685049","wikidata":"https://www.wikidata.org/wiki/Q4454941","display_name":"Euclidean minimum spanning tree","level":4,"score":0.7710875272750854},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.6980384588241577},{"id":"https://openalex.org/C63645285","wikidata":"https://www.wikidata.org/wiki/Q797860","display_name":"Kruskal's algorithm","level":3,"score":0.6720007061958313},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5879135131835938},{"id":"https://openalex.org/C58581272","wikidata":"https://www.wikidata.org/wiki/Q12741163","display_name":"Workspace","level":3,"score":0.5135972499847412},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5132761001586914},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5077358484268188},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4890631139278412},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4833680987358093},{"id":"https://openalex.org/C64271015","wikidata":"https://www.wikidata.org/wiki/Q6865444","display_name":"Minimum degree spanning tree","level":3,"score":0.48007112741470337},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.46016380190849304},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4550950229167938},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4432704448699951},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44051510095596313},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.42855381965637207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3799639642238617},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3662082850933075},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12610793113708496},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.08827334642410278},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:arXiv.org:1712.06431","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.06431","pdf_url":"https://arxiv.org/pdf/1712.06431","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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:ojs.library.carleton.ca:article/3111","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3111","pdf_url":"https://jocg.org/index.php/jocg/article/view/3111","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 11 No. 1 (2020); 525\u2013547","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/495122","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/495122","pdf_url":"http://hdl.handle.net/20.500.11850/495122","source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry, 11 (1)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.48550/arxiv.1712.06431","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1712.06431","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.20382/jocg.v11i1a21","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v11i1a21","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.3929/ethz-b-000495122","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000495122","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1712.06431","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.06431","pdf_url":"https://arxiv.org/pdf/1712.06431","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[{"score":0.41999998688697815,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1065468951","display_name":null,"funder_award_id":"MU/3501/2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8526424774","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1527197079","https://openalex.org/W1889754528","https://openalex.org/W1978331593","https://openalex.org/W1983266860","https://openalex.org/W1990160390","https://openalex.org/W2001552595","https://openalex.org/W2039511348","https://openalex.org/W2049516232","https://openalex.org/W2063295648","https://openalex.org/W2103678784","https://openalex.org/W2105448807","https://openalex.org/W2106424477","https://openalex.org/W2149906774","https://openalex.org/W2158382416","https://openalex.org/W2163227453","https://openalex.org/W2200983654","https://openalex.org/W2296295447","https://openalex.org/W2406481306","https://openalex.org/W2729633485","https://openalex.org/W2963304352","https://openalex.org/W2963964459","https://openalex.org/W3023264955","https://openalex.org/W3041834803","https://openalex.org/W3098373462","https://openalex.org/W3124387147","https://openalex.org/W3145128584"],"related_works":["https://openalex.org/W2943635264","https://openalex.org/W1561849181","https://openalex.org/W4380840098","https://openalex.org/W2418231958","https://openalex.org/W2518240130","https://openalex.org/W3081212354","https://openalex.org/W2387385213","https://openalex.org/W1985149601","https://openalex.org/W2048177396","https://openalex.org/W88291963"],"abstract_inverted_index":{"$\\newcommand{\\EMST}{\\mathrm{EMST}}\\newcommand{\\RNG}{\\mathrm{RNG}}$We":[0],"present":[1],"time-space":[2],"trade-offs":[3],"for":[4,82,99,134,142],"computing":[5],"the":[6,19,40,70,80,94,128,153,166,201,204,210],"Euclidean":[7,41],"minimum":[8,42,167,206],"spanning":[9,43,168,207],"tree":[10,44,169],"of":[11,15,39,76,121,158,170,182,190,203],"a":[12,29,61,124,162,187],"set":[13],"$S$":[14,26],"$n$":[16],"point-sites":[17],"in":[18,28,113],"plane.":[20],"More":[21],"precisely,":[22],"we":[23,148,184],"assume":[24],"that":[25,32,69,92,165],"resides":[27],"random-access":[30],"memory":[31,78],"can":[33],"only":[34],"be":[35,48,54],"read.":[36],"The":[37],"edges":[38,211],"$\\EMST(S)$":[45,112],"have":[46],"to":[47,88,110,196],"reported":[49],"sequentially,":[50],"and":[51,105,138,199],"they":[52],"cannot":[53],"accessed":[55],"or":[56],"modified":[57],"afterwards.":[58],"There":[59],"is":[60,87,161,172],"parameter":[62],"$s":[63,135,143],"\\in":[64],"\\{1,":[65],"\\dots,":[66],"n\\}$":[67],"so":[68],"algorithm":[71,91,151,178],"may":[72],"use":[73],"$O(s)$":[74,119,180],"cells":[75,120,181],"read-write":[77],"(called":[79],"workspace)":[81],"its":[83],"computations.":[84],"Our":[85],"goal":[86],"find":[89],"an":[90],"has":[93],"best":[95,130],"possible":[96],"running":[97],"time":[98,117],"any":[100],"given":[101],"$s$":[102],"between":[103,127],"$1$":[104],"$n$.":[106],"We":[107],"show":[108],"how":[109],"compute":[111],"$O\\big((n^3/s^2)\\log":[114],"s":[115],"\\big)$":[116],"with":[118,179],"workspace,":[122,183],"giving":[123],"smooth":[125],"trade-off":[126],"two":[129],"known":[131],"bounds":[132],"$O(n^3)$":[133],"=":[136,144],"1$":[137],"$O(n":[139],"\\log":[140],"n)$":[141],"n$.":[145],"For":[146],"this,":[147],"run":[149],"Kruskal's":[150,177],"on":[152],"relative":[154],"neighborhood":[155],"graph":[156],"(RNG)":[157],"$S$.":[159],"It":[160],"classic":[163],"fact":[164],"$\\RNG(S)$":[171],"exactly":[173],"$\\EMST(S)$.":[174],"To":[175],"implement":[176],"define":[185],"\\emph{$s$-nets},":[186],"compact":[188],"representation":[189],"planar":[191],"graphs.":[192],"This":[193],"allows":[194],"us":[195],"efficiently":[197],"maintain":[198],"update":[200],"components":[202],"current":[205],"forest":[208],"as":[209],"are":[212],"being":[213],"inserted.":[214]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2018-01-05T00:00:00"}