{"id":"https://openalex.org/W4298008751","doi":"https://doi.org/10.1137/22m1502707","title":"Euclidean Steiner Spanners: Light and Sparse","display_name":"Euclidean Steiner Spanners: Light and Sparse","publication_year":2022,"publication_date":"2022-09-01","ids":{"openalex":"https://openalex.org/W4298008751","doi":"https://doi.org/10.1137/22m1502707"},"language":"en","primary_location":{"id":"doi:10.1137/22m1502707","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1502707","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5072487585","display_name":"Sujoy Bhore","orcid":"https://orcid.org/0000-0003-0104-1659"},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]},{"id":"https://openalex.org/I157638225","display_name":"California State University, Northridge","ror":"https://ror.org/005f5hv41","country_code":"US","type":"education","lineage":["https://openalex.org/I157638225"]},{"id":"https://openalex.org/I288749910","display_name":"Indian Institute of Science Education and Research, Bhopal","ror":"https://ror.org/02rb21j89","country_code":"IN","type":"education","lineage":["https://openalex.org/I288749910"]}],"countries":["IN","US"],"is_corresponding":false,"raw_author_name":"Sujoy Bhore","raw_affiliation_strings":["California State University Northridge, Los Angeles, CA; and","Indian Institute of Science Education and Research, Bhopal, India","Tufts University, Medford, MA, USA"],"raw_orcid":"https://orcid.org/0000-0003-0104-1659","affiliations":[{"raw_affiliation_string":"California State University Northridge, Los Angeles, CA; and","institution_ids":["https://openalex.org/I157638225"]},{"raw_affiliation_string":"Indian Institute of Science Education and Research, Bhopal, India","institution_ids":["https://openalex.org/I288749910"]},{"raw_affiliation_string":"Tufts University, Medford, MA, USA","institution_ids":["https://openalex.org/I121934306"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030799674","display_name":"Csaba D. T\u00f3th","orcid":"https://orcid.org/0000-0002-8769-3190"},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]},{"id":"https://openalex.org/I157638225","display_name":"California State University, Northridge","ror":"https://ror.org/005f5hv41","country_code":"US","type":"education","lineage":["https://openalex.org/I157638225"]},{"id":"https://openalex.org/I288749910","display_name":"Indian Institute of Science Education and Research, Bhopal","ror":"https://ror.org/02rb21j89","country_code":"IN","type":"education","lineage":["https://openalex.org/I288749910"]}],"countries":["IN","US"],"is_corresponding":false,"raw_author_name":"Csaba D. T\u00f3th","raw_affiliation_strings":["California State University Northridge, Los Angeles, CA; and","Indian Institute of Science Education and Research, Bhopal, India","Tufts University, Medford, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California State University Northridge, Los Angeles, CA; and","institution_ids":["https://openalex.org/I157638225"]},{"raw_affiliation_string":"Indian Institute of Science Education and Research, Bhopal, India","institution_ids":["https://openalex.org/I288749910"]},{"raw_affiliation_string":"Tufts University, Medford, MA, USA","institution_ids":["https://openalex.org/I121934306"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3031,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.92603483,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"36","issue":"3","first_page":"2411","last_page":"2444"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"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":0.9994999766349792,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9958999752998352,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9847999811172485,"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":0.7536453604698181},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6995818018913269},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6476541757583618},{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.6160889863967896},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4159952402114868},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0997546911239624}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7536453604698181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6995818018913269},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6476541757583618},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.6160889863967896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4159952402114868},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0997546911239624}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1502707","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1502707","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1481010420","https://openalex.org/W1491725382","https://openalex.org/W1505970908","https://openalex.org/W1511442367","https://openalex.org/W1764866826","https://openalex.org/W1969588170","https://openalex.org/W1976125024","https://openalex.org/W1988573007","https://openalex.org/W1991315286","https://openalex.org/W1991530421","https://openalex.org/W1994072278","https://openalex.org/W2002041206","https://openalex.org/W2004476837","https://openalex.org/W2006095056","https://openalex.org/W2011240422","https://openalex.org/W2016064056","https://openalex.org/W2018963243","https://openalex.org/W2031671531","https://openalex.org/W2036114412","https://openalex.org/W2052373622","https://openalex.org/W2079033199","https://openalex.org/W2091569826","https://openalex.org/W2097333461","https://openalex.org/W2113604744","https://openalex.org/W2139391136","https://openalex.org/W2141105412","https://openalex.org/W2160816205","https://openalex.org/W2165274952","https://openalex.org/W2165443404","https://openalex.org/W2167366051","https://openalex.org/W2486666919","https://openalex.org/W2766798115","https://openalex.org/W2774521735","https://openalex.org/W2786889022","https://openalex.org/W2950920490","https://openalex.org/W2953246643","https://openalex.org/W2971434485","https://openalex.org/W3105802762"],"related_works":["https://openalex.org/W3094179009","https://openalex.org/W1971779258","https://openalex.org/W2088497613","https://openalex.org/W2321943612","https://openalex.org/W2968854554","https://openalex.org/W2055362092","https://openalex.org/W2059722209","https://openalex.org/W4293411872","https://openalex.org/W2949065216","https://openalex.org/W3022165982"],"abstract_inverted_index":{"Lightness":[0],"and":[1,19,37,55,77,81,91,110,124,162,181,196,221,253,287,291],"sparsity":[2,78,92,115,182,200],"are":[3,21],"two":[4],"natural":[5],"parameters":[6],"for":[7,69,102,112,118,193,198,207,244,271],"Euclidean":[8,44,184,205,260],"$(1+\\varepsilon)$-spanners.":[9,186],"Classical":[10],"results":[11],"show":[12,242],"that,":[13],"when":[14],"the":[15,43,64,74,89,103,113,145,151,157,160,163,179,194,199,224,236,251,268,275],"dimension":[16],"$d\\in":[17,71],"\\mathbb{N}$":[18],"$\\varepsilon>0$":[20],"constant,":[22],"every":[23,245,254],"set":[24,247],"$S$":[25],"of":[26,42,48,58,73,79,93,100,141,153,169,183,191,201,238,248,263,277,284],"$n$":[27],"points":[28,85,249],"in":[29,106,116,144,204,250],"$d$-space":[30,117,206],"admits":[31],"a":[32,51,94,167,259,292,299],"$(1+\\varepsilon)$-spanner":[33,262],"with":[34],"$O(n)$":[35],"edges":[36],"weight":[38,301],"proportional":[39],"to":[40,297],"that":[41,83,243],"minimum":[45,75,104,114,164],"spanning":[46],"tree":[47],"$S$.":[49],"In":[50,171],"recent":[52],"breakthrough,":[53],"Le":[54,123,220],"Solomon":[56,125],"[Proceedings":[57],"FOCS,":[59],"2019,":[60],"pp.":[61,136],"1078--1100]":[62],"established":[63],"precise":[65],"dependencies":[66],"on":[67,178,235],"$\\varepsilon>0$,":[68],"constant":[70,209],"\\mathbb{N}$,":[72],"lightness":[76,90,105,142,180,195,264],"$(1+\\varepsilon)$-spanners,":[80],"observed":[82],"Steiner":[84,139,185,261],"can":[86],"substantially":[87,226],"improve":[88,175],"$(1+\\varepsilon)$-spanner.":[95],"They":[96],"gave":[97],"upper":[98],"bounds":[99,177,190],"$\\tilde{O}(\\varepsilon^{-(d+1)/2})$":[101],"dimensions":[107],"$d\\geq":[108,120,210],"3$":[109],"$\\tilde{O}(\\varepsilon^{-(d-1)/2})$":[111],"all":[119,208],"1$.":[121],"Subsequently,":[122],"[LIPIcs":[126],"Leibniz":[127],"Int.":[128],"Proc.":[129],"Inform.":[130],"173,":[131],"Schloss":[132],"Dagstuhl,":[133],"Wadern,":[134],"2020,":[135],"67:1--67:22]":[137],"constructed":[138],"$(1+\\varepsilon)$-spanners":[140],"$O(\\varepsilon^{-1}\\log\\Delta)$":[143],"plane,":[146],"where":[147],"$\\Delta\\in":[148],"\\Omega(\\sqrt{n})$":[149],"is":[150],"spread":[152],"$S$,":[154],"defined":[155],"as":[156],"ratio":[158],"between":[159,166],"maximum":[161],"distance":[165],"pair":[168],"points.":[170],"this":[172,266],"work,":[173,229],"we":[174,241],"several":[176],"We":[187,273],"establish":[188],"lower":[189,213,269],"$\\Omega(\\varepsilon^{-d/2})$":[192],"$\\Omega(\\varepsilon^{-(d-1)/2})$":[197],"such":[202],"spanners":[203,290],"2$.":[211],"Our":[212],"bound":[214,270],"constructions":[215,218],"generalize":[216,274],"previous":[217,228],"by":[219],"Solomon,":[222],"but":[223],"analysis":[225],"simplifies":[227],"using":[230],"new":[231],"geometric":[232],"insight,":[233],"focusing":[234],"directions":[237],"edges.":[239],"Next,":[240],"finite":[246],"plane":[252],"$\\varepsilon\\in":[255],"(0,1]$,":[256],"there":[257],"exists":[258],"$O(\\varepsilon^{-1})$;":[265],"matches":[267],"$d=2$.":[272],"notion":[276],"shallow":[278],"light":[279],"trees,":[280],"which":[281],"may":[282],"be":[283],"independent":[285],"interest,":[286],"use":[288],"directional":[289],"modified":[293],"window":[294],"partitioning":[295],"scheme":[296],"achieve":[298],"tight":[300],"analysis.":[302]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-27T08:26:11.824852","created_date":"2025-10-10T00:00:00"}
