{"id":"https://openalex.org/W2102662973","doi":null,"title":"Approximate shortest path and distance queries in networks","display_name":"Approximate shortest path and distance queries in networks","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2102662973","mag":"2102662973"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.631.4803","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.631.4803","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.sommer.jp/defense.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Christian Sommer","orcid":"https://orcid.org/0000-0002-6641-0681","observed_orcids":["https://orcid.org/0000-0002-6641-0681"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christian Sommer","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6641-0681","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.0284,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.95511162,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"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":0.9984999895095825,"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":0.9984999895095825,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.000699999975040555,"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/T11269","display_name":"Algorithms and Data Compression","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/shortest-path-queries","display_name":"shortest path queries","score":0.8109999895095825},{"id":"https://openalex.org/keywords/distance-oracles","display_name":"distance oracles","score":0.8420000076293945},{"id":"https://openalex.org/keywords/approximate-shortest-paths","display_name":"approximate shortest paths","score":0.902999997138977},{"id":"https://openalex.org/keywords/space-lower-bounds","display_name":"space lower bounds","score":0.7940000295639038},{"id":"https://openalex.org/keywords/scale-free-networks","display_name":"scale-free networks","score":0.7710000276565552},{"id":"https://openalex.org/keywords/complex-networks","display_name":"complex networks","score":0.7570000290870667},{"id":"https://openalex.org/keywords/transportation-networks","display_name":"transportation networks","score":0.8259999752044678},{"id":"https://openalex.org/keywords/social-networks","display_name":"social networks","score":0.8999999761581421},{"id":"https://openalex.org/keywords/random-sampling","display_name":"random sampling","score":0.6620000004768372},{"id":"https://openalex.org/keywords/planar-graphs","display_name":"planar graphs","score":0.8330000042915344}],"concepts":[{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.8108444213867188},{"id":"https://openalex.org/C70266271","wikidata":"https://www.wikidata.org/wiki/Q6343044","display_name":"K shortest path routing","level":4,"score":0.717897891998291},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6764376759529114},{"id":"https://openalex.org/C159379195","wikidata":"https://www.wikidata.org/wiki/Q7239568","display_name":"Precomputation","level":3,"score":0.6442819237709045},{"id":"https://openalex.org/C178067994","wikidata":"https://www.wikidata.org/wiki/Q1128278","display_name":"Constrained Shortest Path First","level":5,"score":0.476581335067749},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.47410470247268677},{"id":"https://openalex.org/C168451585","wikidata":"https://www.wikidata.org/wiki/Q7502159","display_name":"Shortest Path Faster Algorithm","level":5,"score":0.4684484302997589},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4546249210834503},{"id":"https://openalex.org/C170836113","wikidata":"https://www.wikidata.org/wiki/Q5406126","display_name":"Euclidean shortest path","level":5,"score":0.4506148099899292},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.44471219182014465},{"id":"https://openalex.org/C186065694","wikidata":"https://www.wikidata.org/wiki/Q1047576","display_name":"Floyd\u2013Warshall algorithm","level":5,"score":0.42642703652381897},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3554866313934326},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2604871690273285},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2439548671245575},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.13017705082893372},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.07705190777778625},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.06879103183746338}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.631.4803","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.631.4803","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.sommer.jp/defense.pdf","raw_type":"text"},{"id":"mag:2102662973","doi":null,"is_oa":false,"landing_page_url":"https://www.shortestpaths.com/csom_phdthesis.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":663,"referenced_works":["https://openalex.org/W27247825","https://openalex.org/W30435042","https://openalex.org/W37920525","https://openalex.org/W42546367","https://openalex.org/W46283848","https://openalex.org/W56195181","https://openalex.org/W59750408","https://openalex.org/W63310685","https://openalex.org/W72529835","https://openalex.org/W85206208","https://openalex.org/W101508493","https://openalex.org/W104675468","https://openalex.org/W111038805","https://openalex.org/W119035131","https://openalex.org/W138990788","https://openalex.org/W140456478","https://openalex.org/W140737195","https://openalex.org/W155417673","https://openalex.org/W161392887","https://openalex.org/W171462922","https://openalex.org/W177721096","https://openalex.org/W181128013","https://openalex.org/W198692012","https://openalex.org/W272982077","https://openalex.org/W326304601","https://openalex.org/W331362054","https://openalex.org/W433791451","https://openalex.org/W638149299","https://openalex.org/W1480135873","https://openalex.org/W1480718878","https://openalex.org/W1483025564","https://openalex.org/W1487146975","https://openalex.org/W1488981024","https://openalex.org/W1491427870","https://openalex.org/W1493214567","https://openalex.org/W1495355927","https://openalex.org/W1497536023","https://openalex.org/W1498464051","https://openalex.org/W1501936286","https://openalex.org/W1502577746","https://openalex.org/W1503428008","https://openalex.org/W1505815330","https://openalex.org/W1505842299","https://openalex.org/W1507556857","https://openalex.org/W1508228715","https://openalex.org/W1509639714","https://openalex.org/W1511279056","https://openalex.org/W1514499253","https://openalex.org/W1515193333","https://openalex.org/W1516511690","https://openalex.org/W1520740947","https://openalex.org/W1521472129","https://openalex.org/W1525292321","https://openalex.org/W1527104720","https://openalex.org/W1527270374","https://openalex.org/W1527483699","https://openalex.org/W1528485123","https://openalex.org/W1530239281","https://openalex.org/W1532372175","https://openalex.org/W1532922475","https://openalex.org/W1533788422","https://openalex.org/W1534623532","https://openalex.org/W1536245096","https://openalex.org/W1538399680","https://openalex.org/W1548130489","https://openalex.org/W1548756387","https://openalex.org/W1549231754","https://openalex.org/W1549911051","https://openalex.org/W1550136763","https://openalex.org/W1551635709","https://openalex.org/W1553128009","https://openalex.org/W1554238760","https://openalex.org/W1555787662","https://openalex.org/W1555807285","https://openalex.org/W1556485156","https://openalex.org/W1557044085","https://openalex.org/W1557457104","https://openalex.org/W1561240874","https://openalex.org/W1561732644","https://openalex.org/W1564010364","https://openalex.org/W1564357124","https://openalex.org/W1567047166","https://openalex.org/W1568439642","https://openalex.org/W1572272766","https://openalex.org/W1572758096","https://openalex.org/W1573579329","https://openalex.org/W1575027696","https://openalex.org/W1575510715","https://openalex.org/W1579606576","https://openalex.org/W1581228220","https://openalex.org/W1582106056","https://openalex.org/W1582742149","https://openalex.org/W1583205259","https://openalex.org/W1583434898","https://openalex.org/W1583452899","https://openalex.org/W1589566040","https://openalex.org/W1589629289","https://openalex.org/W1591816673","https://openalex.org/W1591854528","https://openalex.org/W1593263981","https://openalex.org/W1595943972","https://openalex.org/W1597567432","https://openalex.org/W1597747553","https://openalex.org/W1599325086","https://openalex.org/W1599935894","https://openalex.org/W1650797637","https://openalex.org/W1671030380","https://openalex.org/W1671881141","https://openalex.org/W1671906456","https://openalex.org/W1673383737","https://openalex.org/W1697432253","https://openalex.org/W1715359176","https://openalex.org/W1715975119","https://openalex.org/W1792949193","https://openalex.org/W1810931192","https://openalex.org/W1823654214","https://openalex.org/W1846138756","https://openalex.org/W1854194788","https://openalex.org/W1854214752","https://openalex.org/W1866249310","https://openalex.org/W1869733865","https://openalex.org/W1873883066","https://openalex.org/W1876661458","https://openalex.org/W1953975752","https://openalex.org/W1964416868","https://openalex.org/W1964915778","https://openalex.org/W1964948588","https://openalex.org/W1965109038","https://openalex.org/W1965216219","https://openalex.org/W1965469937","https://openalex.org/W1967005434","https://openalex.org/W1967359086","https://openalex.org/W1967507014","https://openalex.org/W1967570846","https://openalex.org/W1969229778","https://openalex.org/W1969357318","https://openalex.org/W1969483458","https://openalex.org/W1969573308","https://openalex.org/W1969668378","https://openalex.org/W1970394074","https://openalex.org/W1970606193","https://openalex.org/W1971052845","https://openalex.org/W1971101765","https://openalex.org/W1971316210","https://openalex.org/W1971421925","https://openalex.org/W1971470866","https://openalex.org/W1972414329","https://openalex.org/W1972920042","https://openalex.org/W1972969203","https://openalex.org/W1972978715","https://openalex.org/W1973749534","https://openalex.org/W1974358136","https://openalex.org/W1974395471","https://openalex.org/W1974850750","https://openalex.org/W1974880055","https://openalex.org/W1976969221","https://openalex.org/W1977138516","https://openalex.org/W1977421134","https://openalex.org/W1978757752","https://openalex.org/W1979232449","https://openalex.org/W1979656812","https://openalex.org/W1979740015","https://openalex.org/W1980223785","https://openalex.org/W1980347321","https://openalex.org/W1980480824","https://openalex.org/W1981234161","https://openalex.org/W1982180670","https://openalex.org/W1982184342","https://openalex.org/W1983345514","https://openalex.org/W1984495995","https://openalex.org/W1985177045","https://openalex.org/W1985241583","https://openalex.org/W1985248597","https://openalex.org/W1985324218","https://openalex.org/W1985327268","https://openalex.org/W1986602944","https://openalex.org/W1987236914","https://openalex.org/W1987503114","https://openalex.org/W1987669032","https://openalex.org/W1987983010","https://openalex.org/W1988067232","https://openalex.org/W1988183975","https://openalex.org/W1989575783","https://openalex.org/W1989894867","https://openalex.org/W1990317614","https://openalex.org/W1991225280","https://openalex.org/W1991351021","https://openalex.org/W1991755800","https://openalex.org/W1991809067","https://openalex.org/W1991836779","https://openalex.org/W1993022201","https://openalex.org/W1993286459","https://openalex.org/W1993328543","https://openalex.org/W1993643838","https://openalex.org/W1993803315","https://openalex.org/W1993901614","https://openalex.org/W1994924587","https://openalex.org/W1995713768","https://openalex.org/W1995951476","https://openalex.org/W1996028864","https://openalex.org/W1996722412","https://openalex.org/W1997027778","https://openalex.org/W1997096494","https://openalex.org/W1997369416","https://openalex.org/W1997413504","https://openalex.org/W1997679949","https://openalex.org/W1997883861","https://openalex.org/W1998544343","https://openalex.org/W1999222448","https://openalex.org/W1999244633","https://openalex.org/W1999478155","https://openalex.org/W1999545213","https://openalex.org/W2000234319","https://openalex.org/W2000480596","https://openalex.org/W2000558287","https://openalex.org/W2000836282","https://openalex.org/W2000879295","https://openalex.org/W2001075173","https://openalex.org/W2001811808","https://openalex.org/W2002039869","https://openalex.org/W2002041206","https://openalex.org/W2002501531","https://openalex.org/W2002762033","https://openalex.org/W2002838096","https://openalex.org/W2002874178","https://openalex.org/W2003207175","https://openalex.org/W2003457914","https://openalex.org/W2003757877","https://openalex.org/W2003969379","https://openalex.org/W2004322147","https://openalex.org/W2005314985","https://openalex.org/W2005985615","https://openalex.org/W2006383304","https://openalex.org/W2006423444","https://openalex.org/W2006570180","https://openalex.org/W2006830086","https://openalex.org/W2007575140","https://openalex.org/W2007695015","https://openalex.org/W2007811843","https://openalex.org/W2007903903","https://openalex.org/W2008138618","https://openalex.org/W2008440715","https://openalex.org/W2008620264","https://openalex.org/W2009248757","https://openalex.org/W2009303970","https://openalex.org/W2009852526","https://openalex.org/W2009906570","https://openalex.org/W2010601538","https://openalex.org/W2013627567","https://openalex.org/W2013849999","https://openalex.org/W2014211132","https://openalex.org/W2014317399","https://openalex.org/W2014348203","https://openalex.org/W2014411916","https://openalex.org/W2014635219","https://openalex.org/W2014777750","https://openalex.org/W2014889099","https://openalex.org/W2015326607","https://openalex.org/W2015648019","https://openalex.org/W2017274979","https://openalex.org/W2017975254","https://openalex.org/W2018045523","https://openalex.org/W2018047324","https://openalex.org/W2018480107","https://openalex.org/W2018493433","https://openalex.org/W2020147819","https://openalex.org/W2020556531","https://openalex.org/W2020622763","https://openalex.org/W2020730893","https://openalex.org/W2020965855","https://openalex.org/W2022783258","https://openalex.org/W2022980325","https://openalex.org/W2023367804","https://openalex.org/W2023552332","https://openalex.org/W2023624803","https://openalex.org/W2025397044","https://openalex.org/W2025535442","https://openalex.org/W2025564919","https://openalex.org/W2025844353","https://openalex.org/W2026042206","https://openalex.org/W2026709222","https://openalex.org/W2027011267","https://openalex.org/W2027377866","https://openalex.org/W2027428596","https://openalex.org/W2027580688","https://openalex.org/W2028166348","https://openalex.org/W2028274788","https://openalex.org/W2028293948","https://openalex.org/W2028341270","https://openalex.org/W2028558845","https://openalex.org/W2029132631","https://openalex.org/W2029448190","https://openalex.org/W2030178622","https://openalex.org/W2030267609","https://openalex.org/W2030331592","https://openalex.org/W2030539428","https://openalex.org/W2030874472","https://openalex.org/W2031564644","https://openalex.org/W2031874971","https://openalex.org/W2032324603","https://openalex.org/W2033405938","https://openalex.org/W2034501275","https://openalex.org/W2034680223","https://openalex.org/W2035316056","https://openalex.org/W2035476608","https://openalex.org/W2035494495","https://openalex.org/W2035713940","https://openalex.org/W2036307254","https://openalex.org/W2036871172","https://openalex.org/W2038142281","https://openalex.org/W2038195874","https://openalex.org/W2038504986","https://openalex.org/W2038964811","https://openalex.org/W2039464620","https://openalex.org/W2039498863","https://openalex.org/W2040712217","https://openalex.org/W2040941311","https://openalex.org/W2041618693","https://openalex.org/W2042439821","https://openalex.org/W2043092105","https://openalex.org/W2043396212","https://openalex.org/W2043655327","https://openalex.org/W2044265267","https://openalex.org/W2045446569","https://openalex.org/W2045851525","https://openalex.org/W2047399896","https://openalex.org/W2047940964","https://openalex.org/W2048096483","https://openalex.org/W2048324994","https://openalex.org/W2048824634","https://openalex.org/W2048941791","https://openalex.org/W2049016755","https://openalex.org/W2049500052","https://openalex.org/W2050108834","https://openalex.org/W2050289388","https://openalex.org/W2050532143","https://openalex.org/W2051311803","https://openalex.org/W2051790896","https://openalex.org/W2052373622","https://openalex.org/W2052703084","https://openalex.org/W2053578961","https://openalex.org/W2053723217","https://openalex.org/W2054011861","https://openalex.org/W2054523876","https://openalex.org/W2055656009","https://openalex.org/W2056380633","https://openalex.org/W2056403031","https://openalex.org/W2057112598","https://openalex.org/W2057505998","https://openalex.org/W2057886711","https://openalex.org/W2057994027","https://openalex.org/W2058374373","https://openalex.org/W2058426370","https://openalex.org/W2058605898","https://openalex.org/W2058610742","https://openalex.org/W2058937865","https://openalex.org/W2058956837","https://openalex.org/W2059014957","https://openalex.org/W2059608229","https://openalex.org/W2059973026","https://openalex.org/W2060322444","https://openalex.org/W2060484689","https://openalex.org/W2060919812","https://openalex.org/W2060963839","https://openalex.org/W2061135810","https://openalex.org/W2061159212","https://openalex.org/W2061342454","https://openalex.org/W2061771414","https://openalex.org/W2062254828","https://openalex.org/W2063048655","https://openalex.org/W2063301486","https://openalex.org/W2063793224","https://openalex.org/W2064284095","https://openalex.org/W2065304353","https://openalex.org/W2065474496","https://openalex.org/W2065714066","https://openalex.org/W2065759448","https://openalex.org/W2066732937","https://openalex.org/W2069153192","https://openalex.org/W2070207525","https://openalex.org/W2070486524","https://openalex.org/W2070722739","https://openalex.org/W2070928556","https://openalex.org/W2071362870","https://openalex.org/W2071717275","https://openalex.org/W2072064573","https://openalex.org/W2072284820","https://openalex.org/W2072526459","https://openalex.org/W2072876810","https://openalex.org/W2072985157","https://openalex.org/W2073558110","https://openalex.org/W2074286662","https://openalex.org/W2076109400","https://openalex.org/W2076171427","https://openalex.org/W2077383738","https://openalex.org/W2077824753","https://openalex.org/W2078443814","https://openalex.org/W2078980460","https://openalex.org/W2080450835","https://openalex.org/W2081253227","https://openalex.org/W2081580553","https://openalex.org/W2082538734","https://openalex.org/W2083019227","https://openalex.org/W2083093303","https://openalex.org/W2083278411","https://openalex.org/W2083355299","https://openalex.org/W2083534148","https://openalex.org/W2083669067","https://openalex.org/W2084224084","https://openalex.org/W2084297766","https://openalex.org/W2085449715","https://openalex.org/W2085630237","https://openalex.org/W2085761620","https://openalex.org/W2085917651","https://openalex.org/W2086729610","https://openalex.org/W2087219647","https://openalex.org/W2087392909","https://openalex.org/W2087806988","https://openalex.org/W2088062845","https://openalex.org/W2089026470","https://openalex.org/W2089338760","https://openalex.org/W2089633648","https://openalex.org/W2090747326","https://openalex.org/W2091466470","https://openalex.org/W2091635795","https://openalex.org/W2092904196","https://openalex.org/W2093480133","https://openalex.org/W2093899598","https://openalex.org/W2093981583","https://openalex.org/W2094622274","https://openalex.org/W2094724468","https://openalex.org/W2095293504","https://openalex.org/W2095681182","https://openalex.org/W2096111774","https://openalex.org/W2096304547","https://openalex.org/W2096607290","https://openalex.org/W2096725637","https://openalex.org/W2096746450","https://openalex.org/W2096848102","https://openalex.org/W2097147952","https://openalex.org/W2097747425","https://openalex.org/W2097956810","https://openalex.org/W2099123195","https://openalex.org/W2100369465","https://openalex.org/W2100586428","https://openalex.org/W2100877554","https://openalex.org/W2101267973","https://openalex.org/W2101415564","https://openalex.org/W2101828567","https://openalex.org/W2102465486","https://openalex.org/W2102563702","https://openalex.org/W2102842495","https://openalex.org/W2103020051","https://openalex.org/W2104043302","https://openalex.org/W2104085672","https://openalex.org/W2104315543","https://openalex.org/W2104586045","https://openalex.org/W2104734478","https://openalex.org/W2105100091","https://openalex.org/W2105310556","https://openalex.org/W2105684914","https://openalex.org/W2105874695","https://openalex.org/W2107218428","https://openalex.org/W2107455488","https://openalex.org/W2107527903","https://openalex.org/W2107681157","https://openalex.org/W2107740972","https://openalex.org/W2107917944","https://openalex.org/W2108283040","https://openalex.org/W2108567935","https://openalex.org/W2108691698","https://openalex.org/W2109256116","https://openalex.org/W2110910366","https://openalex.org/W2111695485","https://openalex.org/W2112090702","https://openalex.org/W2112509609","https://openalex.org/W2113042487","https://openalex.org/W2113276858","https://openalex.org/W2113344124","https://openalex.org/W2113604744","https://openalex.org/W2114220616","https://openalex.org/W2114365471","https://openalex.org/W2114734373","https://openalex.org/W2115992646","https://openalex.org/W2116407208","https://openalex.org/W2116812387","https://openalex.org/W2117008259","https://openalex.org/W2117260802","https://openalex.org/W2117495845","https://openalex.org/W2118169763","https://openalex.org/W2119114096","https://openalex.org/W2119874970","https://openalex.org/W2120070962","https://openalex.org/W2120424341","https://openalex.org/W2120450054","https://openalex.org/W2120783268","https://openalex.org/W2121320748","https://openalex.org/W2122431314","https://openalex.org/W2122457875","https://openalex.org/W2124637492","https://openalex.org/W2126160338","https://openalex.org/W2126166149","https://openalex.org/W2126911909","https://openalex.org/W2127151074","https://openalex.org/W2127992497","https://openalex.org/W2128058063","https://openalex.org/W2129620481","https://openalex.org/W2130426318","https://openalex.org/W2130725973","https://openalex.org/W2130790725","https://openalex.org/W2130978632","https://openalex.org/W2131099807","https://openalex.org/W2131237536","https://openalex.org/W2132044905","https://openalex.org/W2132051999","https://openalex.org/W2132108235","https://openalex.org/W2132275989","https://openalex.org/W2132582966","https://openalex.org/W2132750992","https://openalex.org/W2132877272","https://openalex.org/W2133768189","https://openalex.org/W2135378328","https://openalex.org/W2135674162","https://openalex.org/W2136442765","https://openalex.org/W2137460525","https://openalex.org/W2137582581","https://openalex.org/W2137948437","https://openalex.org/W2138571234","https://openalex.org/W2139230981","https://openalex.org/W2139472381","https://openalex.org/W2140591634","https://openalex.org/W2140883685","https://openalex.org/W2141667528","https://openalex.org/W2141883265","https://openalex.org/W2142253242","https://openalex.org/W2143293839","https://openalex.org/W2144050074","https://openalex.org/W2144844724","https://openalex.org/W2145062394","https://openalex.org/W2147391892","https://openalex.org/W2147393894","https://openalex.org/W2147713365","https://openalex.org/W2148050869","https://openalex.org/W2148606196","https://openalex.org/W2149164858","https://openalex.org/W2149220137","https://openalex.org/W2149964853","https://openalex.org/W2150410057","https://openalex.org/W2150418461","https://openalex.org/W2150470619","https://openalex.org/W2151021662","https://openalex.org/W2151400766","https://openalex.org/W2151601049","https://openalex.org/W2152290683","https://openalex.org/W2152306920","https://openalex.org/W2152512929","https://openalex.org/W2153319198","https://openalex.org/W2154044080","https://openalex.org/W2154201790","https://openalex.org/W2154356512","https://openalex.org/W2154768509","https://openalex.org/W2155048531","https://openalex.org/W2155474419","https://openalex.org/W2155694840","https://openalex.org/W2157760787","https://openalex.org/W2158128075","https://openalex.org/W2158663853","https://openalex.org/W2159394589","https://openalex.org/W2159525520","https://openalex.org/W2160365857","https://openalex.org/W2160495255","https://openalex.org/W2162133399","https://openalex.org/W2163252320","https://openalex.org/W2163485494","https://openalex.org/W2164141517","https://openalex.org/W2164485560","https://openalex.org/W2164727176","https://openalex.org/W2165283038","https://openalex.org/W2165456041","https://openalex.org/W2165461157","https://openalex.org/W2165621523","https://openalex.org/W2166293769","https://openalex.org/W2166542580","https://openalex.org/W2166551367","https://openalex.org/W2166553701","https://openalex.org/W2166739719","https://openalex.org/W2166818331","https://openalex.org/W2167213838","https://openalex.org/W2167262444","https://openalex.org/W2167869241","https://openalex.org/W2168555292","https://openalex.org/W2168941042","https://openalex.org/W2169015768","https://openalex.org/W2169336598","https://openalex.org/W2169354549","https://openalex.org/W2169528473","https://openalex.org/W2169910125","https://openalex.org/W2171574770","https://openalex.org/W2171692650","https://openalex.org/W2171707538","https://openalex.org/W2171901130","https://openalex.org/W2172107427","https://openalex.org/W2172232420","https://openalex.org/W2175110005","https://openalex.org/W2176446742","https://openalex.org/W2184006489","https://openalex.org/W2227557434","https://openalex.org/W2244611312","https://openalex.org/W2251198337","https://openalex.org/W2294345698","https://openalex.org/W2294603245","https://openalex.org/W2295428206","https://openalex.org/W2295913109","https://openalex.org/W2317303422","https://openalex.org/W2318794083","https://openalex.org/W2321932444","https://openalex.org/W2335518054","https://openalex.org/W2338905098","https://openalex.org/W2340787257","https://openalex.org/W2341171179","https://openalex.org/W2399690039","https://openalex.org/W2402598023","https://openalex.org/W2405998887","https://openalex.org/W2439405256","https://openalex.org/W2495528278","https://openalex.org/W2521525497","https://openalex.org/W2548579856","https://openalex.org/W2561843528","https://openalex.org/W2567974767","https://openalex.org/W2569270235","https://openalex.org/W2570577697","https://openalex.org/W2571257893","https://openalex.org/W2580476827","https://openalex.org/W2592570088","https://openalex.org/W2595455297","https://openalex.org/W2618199688","https://openalex.org/W2621446776","https://openalex.org/W2624301084","https://openalex.org/W2752885492","https://openalex.org/W2762935521","https://openalex.org/W2768149714","https://openalex.org/W2770485470","https://openalex.org/W2795857897","https://openalex.org/W2905110430","https://openalex.org/W2907836217","https://openalex.org/W2912647241","https://openalex.org/W2913492813","https://openalex.org/W2918068376","https://openalex.org/W2950627632","https://openalex.org/W2963834565","https://openalex.org/W2965701451","https://openalex.org/W2988480584","https://openalex.org/W3021432251","https://openalex.org/W3103141125","https://openalex.org/W3103362336","https://openalex.org/W3137299218","https://openalex.org/W3138807513","https://openalex.org/W3143219376","https://openalex.org/W3148763405","https://openalex.org/W3198350258","https://openalex.org/W3198470706","https://openalex.org/W4239180782","https://openalex.org/W4244324195"],"related_works":["https://openalex.org/W2019003829","https://openalex.org/W2184665585","https://openalex.org/W7100963619","https://openalex.org/W4299920488","https://openalex.org/W4416685913","https://openalex.org/W2091208704","https://openalex.org/W2274340621","https://openalex.org/W2081863845","https://openalex.org/W2132044905","https://openalex.org/W1985248597"],"abstract_inverted_index":{"Computing":[0],"shortest":[1,46,112,122,131,155,373],"paths":[2,50,113],"in":[3,14,31,114,146],"graphs":[4,260,288,391,399],"is":[5,37,65,79,176,185,189,228,251,298,366],"one":[6,85],"of":[7,44,63,75,106,138,174,181,193,240,243,246,258,278,295,332,338,347,377],"the":[8,42,45,60,104,117,136,150,182,190,194,199,217,221,225,241,249,284],"most":[9],"fundamental":[10],"and":[11,33,110,207,224,324,380,396],"well-studied":[12],"problems":[13],"combinatorial":[15],"optimization.":[16],"Numerous":[17],"real-world":[18],"applications":[19],"have":[20],"stimulated":[21],"research":[22],"investigations":[23],"for":[24,57,82,127,255,286,307,343,360],"more":[25,87],"than":[26,282],"50":[27],"years.":[28],"Finding":[29],"routes":[30],"road":[32],"public":[34],"transportation":[35,394],"networks":[36,395,403],"a":[38,72,90,93,154,299,313,344,367],"classical":[39],"application":[40],"motivating":[41],"study":[43],"path":[47,123,132,156],"problem.":[48],"Shortest":[49],"are":[51,69,198,266],"also":[52,80],"sought":[53],"by":[54,95],"routing":[55],"schemes":[56],"computer":[58],"networks:":[59,84],"transmission":[61],"time":[62,184],"messages":[64],"less":[66,252,397],"when":[67],"they":[68],"sent":[70],"through":[71,98],"short":[73],"sequence":[74],"routers.":[76],"The":[77,291],"problem":[78,105],"relevant":[81],"social":[83,406],"may":[86,134],"likely":[88],"obtain":[89],"favor":[91],"from":[92,393,401],"stranger":[94],"establishing":[96],"contact":[97],"personal":[99],"connections.":[100],"This":[101],"thesis":[102,297],"investigates":[103],"efficiently":[107,274],"computing":[108,128],"exact":[109],"approximate":[111,372],"graphs,":[115,216,247,264],"with":[116,321],"main":[118,293],"focus":[119],"being":[120],"on":[121],"query":[124,151,157,183,195,205,271,327],"processing.":[125],"Strategies":[126],"answers":[129],"to":[130,148,214,231,273,370],"queries":[133],"involve":[135],"use":[137],"pre-computed":[139],"data":[140,167,267,303,341],"structures":[141,168,268,304,342],"(often":[142],"called":[143],"distance":[144,211,235,276,319,358],"oracles)":[145],"order":[147],"improve":[149],"time.":[152],"Designing":[153],"processing":[158],"method":[159,369,385],"raises":[160],"questions":[161],"such":[162,261,302,404],"as:":[163],"How":[164,178,187],"can":[165],"these":[166],"be":[169],"computed":[170],"efficiently?":[171],"What":[172,197],"amount":[173],"storage":[175,222],"necessary?":[177],"much":[179,279],"improvement":[180],"possible?":[186],"good":[188,322],"approximation":[191,208,226],"quality":[192,227],"result?":[196],"tradeoffs":[200],"between":[201,220],"precomputation":[202],"time,":[203,206],"storage,":[204],"quality?":[209],"For":[210,234],"oracles":[212,236,320,359],"applicable":[213],"general":[215,287],"quantitative":[218],"tradeoff":[219,250,285],"requirement":[223],"known":[229],"up":[230],"constant":[232],"factors.":[233],"that":[237,269,301,318,352],"take":[238],"advantage":[239],"properties":[242],"certain":[244],"classes":[245,257],"however,":[248],"well":[253],"understood:":[254],"some":[256],"sparse":[259,309],"as":[262,405],"planar":[263],"there":[265],"enable":[270],"algorithms":[272],"compute":[275,371],"estimates":[277],"higher":[280],"precision":[281,323],"what":[283],"would":[289],"predict.":[290],"first":[292],"contribution":[294,336,365],"this":[296],"proof":[300],"cannot":[305],"exist":[306],"all":[308],"graphs.":[310,362],"We":[311,350],"prove":[312,351],"space":[314],"lower":[315],"bound":[316],"implying":[317],"very":[325],"low":[326],"costs":[328],"require":[329],"large":[330,345],"amounts":[331],"space.":[333],"A":[334,363],"second":[335],"consists":[337],"spaceand":[339],"time-efficient":[340],"family":[346],"complex":[348,402],"networks.":[349,407],"exploiting":[353],"well-connected":[354],"nodes":[355],"yields":[356],"efficient":[357],"scale-free":[361],"third":[364],"practical":[368],"paths.":[374],"By":[375],"means":[376],"random":[378],"sampling":[379],"graph":[381],"Voronoi":[382],"duals,":[383],"our":[384],"successfully":[386],"accommodates":[387],"both":[388],"highly":[389],"structured":[390,398],"stemming":[392,400]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}