{"id":"https://openalex.org/W2133768189","doi":"https://doi.org/10.1137/0222071","title":"Finding the Hidden Path: Time Bounds for All-Pairs Shortest Paths","display_name":"Finding the Hidden Path: Time Bounds for All-Pairs Shortest Paths","publication_year":1993,"publication_date":"1993-12-01","ids":{"openalex":"https://openalex.org/W2133768189","doi":"https://doi.org/10.1137/0222071","mag":"2133768189"},"language":"en","primary_location":{"id":"doi:10.1137/0222071","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0222071","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/A5028448267","display_name":"David R. Karger","orcid":"https://orcid.org/0000-0002-0024-5847"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"David R. Karger","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051658526","display_name":"Daphne Koller","orcid":"https://orcid.org/0000-0002-2361-6479"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daphne Koller","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110062251","display_name":"Steven J. Phillips","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steven J. Phillips","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028448267"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0425,"has_fulltext":false,"cited_by_count":128,"citation_normalized_percentile":{"value":0.78592309,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"22","issue":"6","first_page":"1199","last_page":"1217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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/T11106","display_name":"Data Management and Algorithms","score":0.998199999332428,"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":0.9979000091552734,"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/shortest-path-problem","display_name":"Shortest path problem","score":0.7727824449539185},{"id":"https://openalex.org/keywords/shortest-path-faster-algorithm","display_name":"Shortest Path Faster Algorithm","score":0.7482540607452393},{"id":"https://openalex.org/keywords/yens-algorithm","display_name":"Yen's algorithm","score":0.7272969484329224},{"id":"https://openalex.org/keywords/dijkstras-algorithm","display_name":"Dijkstra's algorithm","score":0.7192679047584534},{"id":"https://openalex.org/keywords/k-shortest-path-routing","display_name":"K shortest path routing","score":0.6945052146911621},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6546944379806519},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5886436700820923},{"id":"https://openalex.org/keywords/suurballes-algorithm","display_name":"Suurballe's algorithm","score":0.5552854537963867},{"id":"https://openalex.org/keywords/floyd\u2013warshall-algorithm","display_name":"Floyd\u2013Warshall algorithm","score":0.5505707859992981},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4560506343841553},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3904084265232086},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37740933895111084},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2659921646118164},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2506343722343445}],"concepts":[{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.7727824449539185},{"id":"https://openalex.org/C168451585","wikidata":"https://www.wikidata.org/wiki/Q7502159","display_name":"Shortest Path Faster Algorithm","level":5,"score":0.7482540607452393},{"id":"https://openalex.org/C119971455","wikidata":"https://www.wikidata.org/wiki/Q8052172","display_name":"Yen's algorithm","level":5,"score":0.7272969484329224},{"id":"https://openalex.org/C173870130","wikidata":"https://www.wikidata.org/wiki/Q8548","display_name":"Dijkstra's algorithm","level":4,"score":0.7192679047584534},{"id":"https://openalex.org/C70266271","wikidata":"https://www.wikidata.org/wiki/Q6343044","display_name":"K shortest path routing","level":4,"score":0.6945052146911621},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6546944379806519},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5886436700820923},{"id":"https://openalex.org/C98779529","wikidata":"https://www.wikidata.org/wiki/Q7650417","display_name":"Suurballe's algorithm","level":5,"score":0.5552854537963867},{"id":"https://openalex.org/C186065694","wikidata":"https://www.wikidata.org/wiki/Q1047576","display_name":"Floyd\u2013Warshall algorithm","level":5,"score":0.5505707859992981},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4560506343841553},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3904084265232086},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37740933895111084},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2659921646118164},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2506343722343445},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0222071","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0222071","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":22,"referenced_works":["https://openalex.org/W1513400187","https://openalex.org/W1969357318","https://openalex.org/W1975638108","https://openalex.org/W1979740015","https://openalex.org/W1996575062","https://openalex.org/W1999261327","https://openalex.org/W2007572995","https://openalex.org/W2007687856","https://openalex.org/W2022980325","https://openalex.org/W2027580688","https://openalex.org/W2028341270","https://openalex.org/W2051213257","https://openalex.org/W2059014957","https://openalex.org/W2065759448","https://openalex.org/W2084224084","https://openalex.org/W2085917651","https://openalex.org/W2093899598","https://openalex.org/W2115049345","https://openalex.org/W2152506249","https://openalex.org/W2169528473","https://openalex.org/W2920997011","https://openalex.org/W4302339081"],"related_works":["https://openalex.org/W651485002","https://openalex.org/W2597144308","https://openalex.org/W2358661218","https://openalex.org/W2100214387","https://openalex.org/W2381419702","https://openalex.org/W2810620529","https://openalex.org/W2348287729","https://openalex.org/W4253588386","https://openalex.org/W2381351584","https://openalex.org/W2352589493"],"abstract_inverted_index":{"The":[0,40],"all-pairs":[1,94],"shortest-paths":[2,95,140,153],"problem":[3,96,141],"in":[4,16,35,61,157],"weighted":[5],"graphs":[6],"is":[7,29,38,42,50,56,97,146],"investigated.":[8],"An":[9,79],"algorithm\u2014the":[10],"Hidden-Paths":[11,108],"Algorithm\u2014that":[12],"finds":[13],"these":[14],"paths":[15],"time":[17,87],"$O(m^":[18],"*":[19,27,54,65],"n":[20],"+":[21],"n^2":[22],"\\log":[23],"n)$,":[24],"where":[25],"$m^":[26,53,64],"$":[28,55],"the":[30,85,93,107,113,139,151],"number":[31],"of":[32,88,115,138,150],"edges":[33],"participating":[34],"shortest":[36],"paths,":[37],"presented.":[39],"algorithm":[41,91],"a":[43,103],"practical":[44],"substitute":[45],"for":[46,72,92],"Dijkstra\u2019s":[47],"algorithm.":[48],"It":[49],"argued":[51],"that":[52,148],"likely":[57],"to":[58],"be":[59],"small":[60],"practice":[62],"since":[63],"=":[66],"O(n\\log":[67],"n)$":[68],"with":[69],"high":[70],"probability":[71,74],"many":[73,149],"distributions":[75],"on":[76,84],"edge":[77],"weights.":[78],"$\\Omega":[80],"(mn)$":[81],"lower":[82],"bound":[83],"running":[86],"any":[89],"path-comparison-based":[90],"also":[98],"proved.":[99],"Path-comparison-based":[100],"algorithms":[101,114,154],"form":[102],"natural":[104],"class":[105],"containing":[106],"Algorithm,":[109],"as":[110,112],"well":[111],"E.":[116],"W.":[117,127],"Dijkstra":[118],"[Numer.":[119],"Math.,":[120],"1":[121],"(1959),":[122],"pp.":[123],"269\u2013271]":[124],"and":[125,144],"R.":[126],"Floyd":[128],"[Comm.":[129],"ACM,":[130],"5":[131],"(1962),":[132],"p.":[133],"345].":[134],"Lastly,":[135],"generalized":[136],"forms":[137],"are":[142,155],"considered,":[143],"it":[145],"shown":[147],"standard":[152],"effective":[156],"this":[158],"more":[159],"general":[160],"setting.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}