{"id":"https://openalex.org/W2097747425","doi":"https://doi.org/10.1137/s0097539794261295","title":"Fast Algorithms for Constructing t-Spanners and Paths with Stretch t","display_name":"Fast Algorithms for Constructing t-Spanners and Paths with Stretch t","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2097747425","doi":"https://doi.org/10.1137/s0097539794261295","mag":"2097747425"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539794261295","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794261295","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/A5026385549","display_name":"Edith Cohen","orcid":"https://orcid.org/0000-0002-3926-8237"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Edith Cohen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026385549"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7145,"has_fulltext":false,"cited_by_count":176,"citation_normalized_percentile":{"value":0.93226121,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"28","issue":"1","first_page":"210","last_page":"236"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9991999864578247,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8119302988052368},{"id":"https://openalex.org/keywords/spanner","display_name":"Spanner","score":0.782709002494812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6422464847564697},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5353380441665649},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.5239006280899048},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.48979759216308594},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45329779386520386},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3444092273712158},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3419727683067322},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1862696409225464},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10819399356842041}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8119302988052368},{"id":"https://openalex.org/C2779585601","wikidata":"https://www.wikidata.org/wiki/Q4049850","display_name":"Spanner","level":2,"score":0.782709002494812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6422464847564697},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5353380441665649},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.5239006280899048},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.48979759216308594},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45329779386520386},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3444092273712158},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3419727683067322},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1862696409225464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10819399356842041},{"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/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0097539794261295","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794261295","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2002041206","https://openalex.org/W2018963243","https://openalex.org/W2042587503","https://openalex.org/W2075862701","https://openalex.org/W2888871578","https://openalex.org/W4245082111"],"related_works":["https://openalex.org/W2949889395","https://openalex.org/W2162831161","https://openalex.org/W4297623464","https://openalex.org/W2126497992","https://openalex.org/W2082551413","https://openalex.org/W3197005352","https://openalex.org/W2079518702","https://openalex.org/W1537274075","https://openalex.org/W2010173517","https://openalex.org/W1611446778"],"abstract_inverted_index":{"The":[0,72],"distance":[1,49],"between":[2,16,50,105],"two":[3],"vertices":[4,110,127,187],"in":[5,33,193,209,229],"a":[6,13,22,148,176,180,201,239,243,269],"weighted":[7,183],"graph":[8,177],"is":[9,24,43,75,82,86,179],"the":[10,19,25,28,31,34,48,77,140,186,194,206,217],"weight":[11,20,42],"of":[12,21,27,30,60,76,109,164,175,182,188,203,226,245,248],"minimum-weight":[14],"path":[15,23,37],"them":[17,274],"(where":[18],"sum":[26],"weights":[29],"edges":[32,184],"path).":[35],"A":[36,173],"has":[38],"stretcht":[39],"if":[40],"its":[41,51],"at":[44,87],"most":[45],"t":[46,74,204],"times":[47],"end":[52],"points.":[53],"We":[54,95,223,255],"present":[55,96],"algorithms":[56,146,262],"that":[57,102,117,191],"compute":[58],"paths":[59,104,119,145],"stretch":[61,73],"$2\\leq":[62],"t\\leq\\log":[63],"n$":[64],"on":[65,162,185,265],"undirected":[66],"graphs":[67],"G=(V,E)":[68],"with":[69,215],"nonnegative":[70],"weights.":[71],"form":[78],"$t=\\beta(2+\\epsilon')$,":[79],"where":[80,132],"$\\beta$":[81],"integral":[83],"and":[84,111,134,147,199,219,268],"$\\epsilon'>0$":[85],"least":[88],"as":[89,91],"large":[90],"some":[92],"fixed":[93,130,235],"$\\epsilon>0$.":[94],"an":[97,112],"$\\tilde{O}((m+k)n^{(2+\\epsilon)/t})$":[98],"time":[99,151,232],"randomized":[100],"algorithm":[101,116,152],"finds":[103,118],"k":[106],"specified":[107,122],"pairs":[108],"$\\tilde{O}((m+ns)n^{2(1+\\log_n":[113],"m+\\epsilon)/t})$":[114],"deterministic":[115],"from":[120,205],"s":[121],"sources":[123],"to":[124,272],"all":[125],"other":[126],"(for":[128,233],"any":[129,234],"$\\epsilon>0$),":[131,236],"n=|V|":[133],"m=|E|.":[135],"This":[136],"improves":[137],"significantly":[138],"over":[139],"slower":[141],"$\\tilde{O}(\\min\\{k,n\\}m)$":[142],"exact":[143],"shortest":[144],"previous":[149],"$\\tilde{O}(mn^{64/t}+kn^{32/t})$":[150],"by":[153],"Awerbuch":[154],"{et":[155],"al.}\\":[156],"[Proc.":[157],"34th":[158],"IEEE":[159],"Annual":[160],"Symposium":[161],"Foundations":[163],"Computer":[165],"Science,":[166],"IEEE,":[167],"Piscataway,":[168],"NJ,":[169],"1993,":[170],"pp.":[171],"638--647].":[172],"t-spanner":[174],"G":[178,189],"set":[181],"such":[190],"distances":[192,208],"spanner":[195],"are":[196,263],"not":[197],"smaller":[198],"within":[200],"factor":[202,244],"corresponding":[207],"G.":[210],"Previous":[211],"work":[212],"was":[213,252],"concerned":[214],"bounding":[216],"size":[218,227],"efficiently":[220],"constructing":[221],"t-spanners.":[222],"construct":[224,273],"t-spanners":[225],"$\\tilde{O}(n^{1+(2+\\epsilon)/t})$":[228],"$\\tilde{O}(mn^{(2+\\epsilon)/t})$":[230],"expected":[231],"which":[237],"constitutes":[238],"faster":[240],"construction":[241],"(by":[242],"n3+2/t":[246],"/m)":[247],"sparser":[249],"spanners":[250],"than":[251],"previously":[253],"attainable.":[254],"also":[256],"provide":[257],"efficient":[258],"parallel":[259],"constructions.":[260],"Our":[261],"based":[264],"pairwise":[266],"covers":[267],"novel":[270],"approach":[271],"efficiently.":[275]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}