{"id":"https://openalex.org/W158512953","doi":null,"title":"Optimal and Hereditarily Optimal Realizations of Metric Spaces","display_name":"Optimal and Hereditarily Optimal Realizations of Metric Spaces","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W158512953","mag":"158512953"},"language":"en","primary_location":{"id":"pmh:oai:DiVA.org:uu-8297","doi":null,"is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8297","pdf_url":null,"source":{"id":"https://openalex.org/S4306402042","display_name":"Uppsala University Publications (Uppsala University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I123387679","host_organization_name":"Uppsala University","host_organization_lineage":["https://openalex.org/I123387679"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/doctoralThesis"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070508573","display_name":"Alice Lesser","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alice Lesser","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5070508573"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":7,"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":0.7314000129699707,"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":0.7314000129699707,"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":0.13729999959468842,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.03799999877810478,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/weighted-graphs","display_name":"weighted graphs","score":0.718999981880188},{"id":"https://openalex.org/keywords/tight-span","display_name":"tight span","score":0.7429999709129333},{"id":"https://openalex.org/keywords/shortest-path","display_name":"shortest path","score":0.7860000133514404},{"id":"https://openalex.org/keywords/np-hardness","display_name":"NP-hardness","score":0.6819999814033508},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.5479999780654907}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7926256060600281},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6572868824005127},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.533906102180481},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4917338192462921},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.4439815580844879},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44089120626449585},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3353617191314697},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32128551602363586},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08702370524406433},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:DiVA.org:uu-8297","doi":null,"is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8297","pdf_url":null,"source":{"id":"https://openalex.org/S4306402042","display_name":"Uppsala University Publications (Uppsala University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I123387679","host_organization_name":"Uppsala University","host_organization_lineage":["https://openalex.org/I123387679"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/doctoralThesis"},{"id":"mag:158512953","doi":null,"is_oa":false,"landing_page_url":"http://uu.diva-portal.org/smash/get/diva2:170958/FULLTEXT01","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":{"id":"pmh:oai:DiVA.org:uu-8297","doi":null,"is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8297","pdf_url":null,"source":{"id":"https://openalex.org/S4306402042","display_name":"Uppsala University Publications (Uppsala University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I123387679","host_organization_name":"Uppsala University","host_organization_lineage":["https://openalex.org/I123387679"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/doctoralThesis"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W106168664","https://openalex.org/W174827889","https://openalex.org/W1526962514","https://openalex.org/W1535261556","https://openalex.org/W1597196612","https://openalex.org/W1608151808","https://openalex.org/W1618016804","https://openalex.org/W1697463841","https://openalex.org/W1834060250","https://openalex.org/W1963665209","https://openalex.org/W1966496924","https://openalex.org/W1989964203","https://openalex.org/W1998867815","https://openalex.org/W2003312650","https://openalex.org/W2004079181","https://openalex.org/W2011039300","https://openalex.org/W2021847108","https://openalex.org/W2023542709","https://openalex.org/W2041076979","https://openalex.org/W2041863586","https://openalex.org/W2045504542","https://openalex.org/W2055298722","https://openalex.org/W2057289831","https://openalex.org/W2061396714","https://openalex.org/W2061679412","https://openalex.org/W2063099296","https://openalex.org/W2071211665","https://openalex.org/W2081906987","https://openalex.org/W2082445660","https://openalex.org/W2090139725","https://openalex.org/W2096320713","https://openalex.org/W2144221002","https://openalex.org/W2166838615","https://openalex.org/W2316678074"],"related_works":["https://openalex.org/W597906644","https://openalex.org/W1526962514","https://openalex.org/W7095518293","https://openalex.org/W2054108637","https://openalex.org/W2063099296","https://openalex.org/W1963665209","https://openalex.org/W1993940640","https://openalex.org/W2059107568","https://openalex.org/W7096171483","https://openalex.org/W1989964203"],"abstract_inverted_index":{"This":[0,41],"PhD":[1],"thesis,":[2],"consisting":[3],"of":[4,16,21,68,93,105,122,137,180,189,204,257,265,268,288],"an":[5,18,269],"introduction,":[6],"four":[7],"papers,":[8],"and":[9,35,48,96],"some":[10,238],"supplementary":[11],"results,":[12],"studies":[13],"the":[14,32,69,86,91,102,106,114,120,123,128,135,152,231,253,266,286],"problem":[15,42],"finding":[17],"optimal":[19,61,71,87,172,198,216,239,248,271],"realization":[20,72,88,173,217,240,272],"a":[22,27,74,80,178,187,220,226,242,293],"given":[23],"finite":[24],"metric":[25,129,165],"space:":[26],"weighted":[28,60,197],"graph":[29,75,115],"which":[30,76,193,200,218,291],"preserves":[31],"metric's":[33],"distances":[34],"has":[36,55,79,90],"minimal":[37],"total":[38,82],"edge":[39,83],"weight.":[40],"is":[43,117,131,149,219,275],"known":[44,141],"to":[45,98,119,151],"be":[46,64,175],"NP-hard,":[47],"solutions":[49],"are":[50,201],"not":[51,202],"necessarily":[52],"unique.":[53],"It":[54],"been":[56],"conjectured":[57],"that":[58,113,147,162,262,280],"extremally":[59,196],"realizations":[62,199,249],"may":[63],"found":[65,176],"as":[66,142,177,241,250],"subgraphs":[67,203],"hereditarily":[70],"\u0393d,":[73],"in":[77,244],"general":[78],"higher":[81],"weight":[84],"than":[85],"but":[89],"advantages":[92],"being":[94],"unique,":[95],"possible":[97,255],"construct":[99],"explicitly":[100],"via":[101],"tight":[103,124,295],"span":[104,125,296],"metric.":[107],"In":[108,157,182],"Paper":[109,158,183,223],"I,":[110],"we":[111,160,185,235,260,278],"prove":[112,261,279],"\u0393d":[116,148,274],"equivalent":[118],"1-skeleton":[121],"precisely":[126],"when":[127],"considered":[130],"totally":[132,138],"split-decomposable.":[133],"For":[134],"subset":[136,287],"split-decomposable":[139],"metrics":[140,144,191,290],"consistent":[143,289],"this":[145,281],"implies":[146],"isomorphic":[150],"easily":[153],"constructed":[154],"Buneman":[155],"graph.":[156],"II,":[159],"show":[161],"for":[163,192,207,285],"any":[164,171,263],"on":[166],"at":[167,213],"most":[168],"five":[169],"points,":[170],"can":[174,234],"subgraph":[179,243],"\u0393d.":[181,205],"III":[184],"provide":[186],"series":[188],"counterexamples;":[190],"there":[194,210],"exist":[195],"However,":[206],"these":[208],"examples":[209],"also":[211],"exists":[212],"least":[214],"one":[215],"subgraph.":[221],"Finally,":[222],"IV":[224],"examines":[225],"weakened":[227,282],"conjecture":[228,283],"suggested":[229],"by":[230],"above":[232],"counterexamples:":[233],"always":[236],"find":[237],"\u0393d?":[245],"Defining":[246],"extremal":[247,270],"those":[251],"having":[252],"maximum":[254],"number":[256],"shortest":[258],"paths,":[259],"embedding":[264],"vertices":[267],"into":[273],"injective.":[276],"Moreover,":[277],"holds":[284],"have":[292],"2-dimensional":[294]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-09-04T10:56:28.161419","created_date":"2016-06-24T00:00:00"}
