{"id":"https://openalex.org/W7160285099","doi":"https://doi.org/10.48550/arxiv.2605.02114","title":"Undirected Replacement Paths: Dual Fault Reduces to Single Source","display_name":"Undirected Replacement Paths: Dual Fault Reduces to Single Source","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W7160285099","doi":"https://doi.org/10.48550/arxiv.2605.02114"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.02114","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02114","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.02114","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135335238","display_name":"Jakob Nogler","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nogler, Jakob","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044244682","display_name":"Virginia Vassilevska Williams","orcid":"https://orcid.org/0000-0003-4844-2863"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Williams, Virginia Vassilevska","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.8626999855041504,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.8626999855041504,"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":0.09239999949932098,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.004399999976158142,"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/undirected-graph","display_name":"Undirected graph","score":0.7074000239372253},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5730000138282776},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4896000027656555},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4821000099182129},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.4754999876022339},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.45879998803138733},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.45559999346733093},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.45010000467300415}],"concepts":[{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.7074000239372253},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5782999992370605},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5730000138282776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49079999327659607},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4896000027656555},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4821000099182129},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4754999876022339},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4634000062942505},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.45879998803138733},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.45559999346733093},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4458000063896179},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4278999865055084},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.3562999963760376},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3418999910354614},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.3411000072956085},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.29580000042915344},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.289900004863739},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2815000116825104},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.2711000144481659},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2694000005722046}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.02114","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02114","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":"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"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.02114","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02114","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Given":[0,45,84],"a":[1,46,50,85,146,157,173,195],"graph":[2,47,86],"and":[3,8,26,49,59,88,92,127,162,273],"two":[4,34,89,114],"fixed":[5],"vertices":[6],"$s$":[7,25,91],"$t$,":[9,93],"the":[10,22,63,76,102,168,185,223,230,259],"Replacement":[11,42,81],"Path":[12],"Problem":[13],"(RP)":[14],"is":[15,30,156,194,211,219],"to":[16,37,201,207],"compute":[17,54,94],"for":[18,55,95,182,226,233,238,251,269,276],"every":[19,56,60,96],"edge":[20,61],"$e$,":[21],"distance":[23,65,104],"between":[24,125],"$t$":[27],"when":[28],"$e$":[29,62],"removed.":[31],"There":[32],"are":[33,140,177],"natural":[35],"extensions":[36],"RP:":[38],"(1)":[39,235],"Single":[40],"Source":[41],"Paths":[43,82],"(SSRP):":[44],"$G$":[48,87],"source":[51],"node":[52],"$s$,":[53],"vertex":[57],"$v$":[58],"$s$-$v$":[64],"in":[66,105,160,163,172,184,240,253,279],"$G":[67,106],"\\setminus":[68,107],"\\{e\\}$.":[69],"That":[70,110],"is,":[71,111],"we":[72,112,221],"do":[73],"not":[74,212],"fix":[75],"target":[77],"anymore.":[78],"(2)":[79,248],"$2$-Fault":[80],"(2-FRP):":[83],"nodes":[90],"pair":[97],"of":[98,117,167,175,191],"edges":[99],"$e,":[100],"e'$":[101],"$s$-$t$":[103],"\\{e,":[108],"e'\\}$.":[109],"consider":[113],"failures":[115],"instead":[116],"one.":[118],"Previously,":[119],"there":[120,139,155],"was":[121],"no":[122,141],"known":[123,169],"reduction":[124,197,218],"SSRP":[126,183],"2-FRP.":[128],"It":[129],"seemed":[130],"plausible":[131],"that":[132,205,228],"2-FRP":[133,144,170,210],"would":[134],"be":[135],"computationally":[136],"harder":[137,213],"because":[138],"settings":[142,176],"where":[143],"admits":[145],"faster":[147],"algorithm":[148],"than":[149,180,214],"SSRP.":[150,215],"In":[151],"directed":[152],"unweighted":[153,270],"graphs":[154,165,271],"provable":[158],"gap":[159],"complexity,":[161],"undirected":[164,199,202],"many":[166],"algorithms":[171,225],"variety":[174],"much":[178],"slower":[179],"those":[181],"same":[186],"setting.":[187],"The":[188],"main":[189],"contribution":[190],"this":[192],"paper":[193],"tight":[196,293],"from":[198],"$2$-FRP":[200,227],"SSRP,":[203],"showing":[204],"contrary":[206],"prior":[208],"intuition,":[209],"As":[216],"our":[217],"weight-preserving,":[220],"obtain":[222],"first":[224],"match":[229],"best-known":[231],"runtimes":[232],"SSRP:":[234],"$\\tilde{O}(M":[236],"n^\u03c9)$":[237],"weights":[239,252,278],"$[1,":[241,254,280],"M]$":[242],"[GVW19],":[243,256],"improving":[244,257,283],"upon":[245,284],"$O(Mn^{2.87})$":[246],"[CZ24];":[247],"$n^3/2^{\u03a9(\\sqrt{\\log":[249],"n})}$":[250],"\\text{poly}(n)]$":[255],"over":[258],"previous":[260],"$n^3\\text{polylog}(n)$":[261],"running":[262],"time":[263,268],"[VWWX22];":[264],"(3)":[265],"$\\tilde{O}(mn^{1/2}+n^{2})$":[266],"combinatorial":[267],"[CC19],":[272],"more":[274],"generally":[275],"rational":[277],"2]$":[281],"[CM20],":[282],"$\\tilde{O}(n^{3-1/18})$":[285],"[CZ24].":[286],"We":[287],"complement":[288],"these":[289],"upper":[290],"bounds":[291,295],"with":[292],"lower":[294],"under":[296],"fine-grained":[297],"hypotheses.":[298]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-06T00:00:00"}