{"id":"https://openalex.org/W3098783518","doi":"https://doi.org/10.1137/22m1511916","title":"Sharp Thresholds in Random Simple Temporal Graphs","display_name":"Sharp Thresholds in Random Simple Temporal Graphs","publication_year":2024,"publication_date":"2024-03-19","ids":{"openalex":"https://openalex.org/W3098783518","doi":"https://doi.org/10.1137/22m1511916","mag":"3098783518"},"language":"en","primary_location":{"id":"doi:10.1137/22m1511916","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1511916","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/A5061412455","display_name":"Arnaud Casteigts","orcid":"https://orcid.org/0000-0002-7819-7013"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["CH","FR"],"is_corresponding":true,"raw_author_name":"Arnaud Casteigts","raw_affiliation_strings":["Computer Science Department, University of Geneva, Geneva, Switzerland. Part of this project was done while the author was at LaBRI, CNRS, University of Bordeaux, France"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of Geneva, Geneva, Switzerland. Part of this project was done while the author was at LaBRI, CNRS, University of Bordeaux, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I114457229","https://openalex.org/I1294671590","https://openalex.org/I4210142254"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008915624","display_name":"Mikhail Raskin","orcid":"https://orcid.org/0000-0002-6660-5673"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I139506611","display_name":"Sciences Po Bordeaux","ror":"https://ror.org/01b5nw197","country_code":"FR","type":"education","lineage":["https://openalex.org/I139506611"]},{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Michael Raskin","raw_affiliation_strings":["LaBRI, CNRS, University of Bordeaux, Bordeaux, France. Part of this project was done while the author was at Department of Informatics, Technical University of Munich, Germany"],"affiliations":[{"raw_affiliation_string":"LaBRI, CNRS, University of Bordeaux, Bordeaux, France. Part of this project was done while the author was at Department of Informatics, Technical University of Munich, Germany","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I139506611","https://openalex.org/I1294671590","https://openalex.org/I4210142254"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055911066","display_name":"Malte Renken","orcid":"https://orcid.org/0000-0002-1450-1901"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Malte Renken","raw_affiliation_strings":["Algorithmics and Computational Complexity group, Technical University of Berlin, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Algorithmics and Computational Complexity group, Technical University of Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047948708","display_name":"Viktor Zamaraev","orcid":"https://orcid.org/0000-0001-5755-4141"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Viktor Zamaraev","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5061412455"],"corresponding_institution_ids":["https://openalex.org/I114457229","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254"],"apc_list":null,"apc_paid":null,"fwci":1.693,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82770861,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"53","issue":"2","first_page":"346","last_page":"388"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9983000159263611,"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"}},"topics":[{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9983000159263611,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9948999881744385,"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/T10246","display_name":"Mobile Ad Hoc Networks","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/simple","display_name":"Simple (philosophy)","score":0.7258175611495972},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46793195605278015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4639562964439392},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46250125765800476},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.45258957147598267},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3374248147010803},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.22285953164100647}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7258175611495972},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46793195605278015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4639562964439392},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46250125765800476},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.45258957147598267},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3374248147010803},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.22285953164100647},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1511916","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1511916","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":[{"id":"https://openalex.org/G1296132067","display_name":null,"funder_award_id":"ANR-16-CE25-0009-03","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3806350710","display_name":null,"funder_award_id":"787367","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G4802279559","display_name":null,"funder_award_id":"NI 369/17","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"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W390146837","https://openalex.org/W649265788","https://openalex.org/W1518080829","https://openalex.org/W1709909086","https://openalex.org/W1746637951","https://openalex.org/W1847535063","https://openalex.org/W1975935977","https://openalex.org/W1984196269","https://openalex.org/W1999678910","https://openalex.org/W2011898573","https://openalex.org/W2013558775","https://openalex.org/W2031541804","https://openalex.org/W2053185121","https://openalex.org/W2059014957","https://openalex.org/W2068601364","https://openalex.org/W2075410688","https://openalex.org/W2086991377","https://openalex.org/W2097725576","https://openalex.org/W2148775522","https://openalex.org/W2157004711","https://openalex.org/W2164988386","https://openalex.org/W2316439312","https://openalex.org/W2335530756","https://openalex.org/W2336317531","https://openalex.org/W2461566632","https://openalex.org/W2489125130","https://openalex.org/W2517791521","https://openalex.org/W2706788079","https://openalex.org/W2741368709","https://openalex.org/W2763510479","https://openalex.org/W2773586560","https://openalex.org/W2962422787","https://openalex.org/W2962680010","https://openalex.org/W2962819912","https://openalex.org/W2963993884","https://openalex.org/W2964299995","https://openalex.org/W2979430184","https://openalex.org/W2998856043","https://openalex.org/W3027725861","https://openalex.org/W3042151004","https://openalex.org/W3080676684","https://openalex.org/W3100918075","https://openalex.org/W3140257771","https://openalex.org/W3157160562","https://openalex.org/W3166547661","https://openalex.org/W3184567057","https://openalex.org/W3199947862","https://openalex.org/W4232097763","https://openalex.org/W4237347223","https://openalex.org/W4246729727","https://openalex.org/W4246895875"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885","https://openalex.org/W2963966623"],"abstract_inverted_index":{".A":[0],"graph":[1,15,21,177,183],"whose":[2],"edges":[3,38,74],"only":[4],"appear":[5],"at":[6,129,145,148,164,325,338,358],"certain":[7],"points":[8],"in":[9,39,79,114,153,225,276,291,331,386,404,411,434],"time":[10],"is":[11,22,31,178,201,206,212,365,369],"called":[12],"a":[13,20,34,43,51,68,86,118,185,207,307,326,366],"temporal":[14,44,56,91,112,186,216,293,305,437],"(among":[16],"other":[17,334],"names).":[18],"Such":[19],"temporally":[23,179,198,262],"connected":[24,32,263],"if":[25],"each":[26,143,173],"ordered":[27],"pair":[28,134],"of":[29,54,72,89,93,102,105,122,135,188,222,248,260,304,316,320],"vertices":[30,136,169],"by":[33,66],"path":[35],"which":[36,200],"traverses":[37],"chronological":[40],"order":[41],"(i.e.,":[42],"path).":[45],"In":[46,124,239],"this":[47,115,341,363],"paper,":[48],"we":[49,126,310,347,371,378,420],"consider":[50],"simple":[52],"model":[53,116],"random":[55,62,69,292,439],"graph,":[57,63],"obtained":[58],"from":[59],"an":[60,422],"Erd\u0151s\u2013R\u00e9nyi":[61],"\\(G\\sim":[64],"G_{n,p}\\),":[65],"considering":[67],"permutation":[70],"\\(\\pi\\)":[71,80],"the":[73,77,90,100,168,176,182,255,258,273,296,302,333,380],"and":[75,96,163,229,252,257,394,409,428],"interpreting":[76],"ranks":[78],"as":[81,193,195,204,407],"presence":[82],"times.":[83],"We":[84],"give":[85],"thorough":[87],"study":[88,303],"connectivity":[92],"such":[94],"graphs":[95,217],"derive":[97],"implications":[98],"for":[99],"existence":[101],"several":[103],"kinds":[104],"sparse":[106],"spanners.":[107],"It":[108],"turns":[109],"out":[110],"that":[111,128,272,312,349,373,398,410],"reachability":[113],"exhibits":[117],"surprisingly":[119],"regular":[120],"sequence":[121],"thresholds.":[123],"particular,":[125],"show":[127,311,348],"\\(p=\\log":[130],"n/n\\),":[131,147,166,340],"any":[132,155,281],"fixed":[133,156],"can":[137,158,170,401],"asymptotically":[138],"almost":[139],"surely":[140],"(a.a.s.)":[141],"reach":[142,160,172],"other;":[144,174],"\\(2\\log":[146],"least":[149],"one":[150],"vertex":[151,328],"(and,":[152],"fact,":[154,240],"vertex)":[157],"a.a.s.":[159,171,337,357],"all":[161,167],"others;":[162],"\\(3\\log":[165],"i.e.,":[175],"connected.":[180],"Furthermore,":[181],"admits":[184],"spanner":[187],"size":[189,223,249,256,317,353],"\\(2n":[190],"+":[191],"o(n)\\)":[192],"soon":[194],"it":[196,374],"becomes":[197],"connected,":[199],"nearly":[202,286],"optimal,":[203],"\\(2n-4\\)":[205],"lower":[208],"bound.":[209],"This":[210],"result":[211,270],"quite":[213],"significant":[214],"because":[215],"do":[218,242],"not":[219,243],"admit":[220,246],"spanners":[221,247,288,306,315,351],"\\(O(n)\\)":[224],"general":[226],"[Kempe,":[227],"Kleinberg,":[228],"Kumar,":[230],"J.":[231],"Comput.":[232],"System":[233],"Sci.,":[234],"64":[235],"(2002),":[236],"pp.":[237,266],"820\u2013842].":[238],"they":[241,414],"even":[244],"always":[245,289],"\\(o(n^2)\\)":[250],"[Axiotis":[251],"Fotakis,":[253],"On":[254],"approximability":[259],"minimum":[261],"subgraphs,":[264],"2016,":[265],"149:1\u2013149:14].":[267],"Thus,":[268],"our":[269,399,426],"implies":[271],"obstructions":[274],"found":[275],"these":[277,405],"works\u2014and":[278],"more":[279],"generally":[280],"non-negligible":[282],"obstruction\u2014are":[283],"statistically":[284],"insignificant:":[285],"optimal":[287,350],"exist":[290,356],"graphs.":[294],"All":[295],"above":[297,381],"thresholds":[298],"are":[299],"sharp.":[300,345],"Carrying":[301],"step":[308],"further,":[309],"pivotal":[313],"spanners\u2014i.e.,":[314],"\\(2n-2\\)":[318],"composed":[319],"two":[321],"spanning":[322],"trees":[323],"glued":[324],"single":[327],"(one":[329],"descending":[330],"time,":[332],"ascending":[335],"subsequently)\u2014exist":[336],"\\(4\\log":[339],"threshold":[342,368],"being":[343],"also":[344,355],"Finally,":[346,419],"(of":[352],"\\(2n-4\\))":[354],"\\(p=4":[359],"\\log":[360],"n/n\\).":[361],"Whether":[362],"value":[364],"sharp":[367],"open;":[370],"conjecture":[372],"is.":[375],"For":[376],"completeness,":[377],"compare":[379],"results":[382,385,400,417,427,431],"to":[383],"existing":[384],"related":[387],"areas,":[388],"including":[389],"edge-ordered":[390],"graphs,":[391],"gossip":[392],"theory,":[393],"population":[395],"protocols,":[396],"showing":[397],"be":[402],"interpreted":[403],"settings":[406],"well":[408],"some":[412],"cases":[413],"improve":[415],"known":[416],"therein.":[418],"discuss":[421],"intriguing":[423],"connection":[424],"between":[425],"Janson's":[429],"celebrated":[430],"on":[432],"percolation":[433],"weighted":[435],"graphs.Keywordsrandom":[436],"graphErdos\u2013Renyi":[438],"graphsharp":[440],"thresholdtemporal":[441],"reachabilitygossiping":[442],"protocoledge-ordered":[443],"graphMSC":[444],"codes05C8068R05":[445]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
