{"id":"https://openalex.org/W2995774564","doi":"https://doi.org/10.17619/unipb/1-816","title":"Classification and approximation of geometric location problems","display_name":"Classification and approximation of geometric location problems","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2995774564","doi":"https://doi.org/10.17619/unipb/1-816","mag":"2995774564"},"language":"en","primary_location":{"id":"pmh:oai:digital.ub.uni-paderborn.de/hs:3201582","is_oa":true,"landing_page_url":"https://digital.ub.uni-paderborn.de/hs/doi/10.17619/UNIPB/1-816","pdf_url":"https://digital.ub.uni-paderborn.de/hs/doi/10.17619/UNIPB/1-816","source":{"id":"https://openalex.org/S4306400179","display_name":"Habilitation Regulations of the Faculty of Mechanical Engineering (University of Paderborn)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I206945453","host_organization_name":"Paderborn University","host_organization_lineage":["https://openalex.org/I206945453"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},"type":"dissertation","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://digital.ub.uni-paderborn.de/hs/doi/10.17619/UNIPB/1-816","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088533271","display_name":"Sascha Brauer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Brauer, Sascha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5088533271"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.156,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56378135,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"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/T12698","display_name":"3D Modeling in Geospatial Applications","score":0.9045000076293945,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12698","display_name":"3D Modeling in Geospatial Applications","score":0.9045000076293945,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4099918007850647},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38653209805488586},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.34546661376953125},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32921668887138367}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4099918007850647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38653209805488586},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.34546661376953125},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32921668887138367}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:digital.ub.uni-paderborn.de/hs:3201582","is_oa":true,"landing_page_url":"https://digital.ub.uni-paderborn.de/hs/doi/10.17619/UNIPB/1-816","pdf_url":"https://digital.ub.uni-paderborn.de/hs/doi/10.17619/UNIPB/1-816","source":{"id":"https://openalex.org/S4306400179","display_name":"Habilitation Regulations of the Faculty of Mechanical Engineering (University of Paderborn)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I206945453","host_organization_name":"Paderborn University","host_organization_lineage":["https://openalex.org/I206945453"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},{"id":"doi:10.17619/unipb/1-816","is_oa":true,"landing_page_url":"https://doi.org/10.17619/unipb/1-816","pdf_url":null,"source":{"id":"https://openalex.org/S4306401930","display_name":"University Library Bielefeld Digital Collections (Bielefeld University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:2995774564","is_oa":false,"landing_page_url":"https://ris.uni-paderborn.de/publication/13679","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:digital.ub.uni-paderborn.de/hs:3201582","is_oa":true,"landing_page_url":"https://digital.ub.uni-paderborn.de/hs/doi/10.17619/UNIPB/1-816","pdf_url":"https://digital.ub.uni-paderborn.de/hs/doi/10.17619/UNIPB/1-816","source":{"id":"https://openalex.org/S4306400179","display_name":"Habilitation Regulations of the Faculty of Mechanical Engineering (University of Paderborn)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I206945453","host_organization_name":"Paderborn University","host_organization_lineage":["https://openalex.org/I206945453"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},"sustainable_development_goals":[{"display_name":"Climate action","score":0.6700000166893005,"id":"https://metadata.un.org/sdg/13"}],"awards":[{"id":"https://openalex.org/G7624910207","display_name":null,"funder_award_id":"BL 314/8-1","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/F4320324816","display_name":"Universit\u00e4t Paderborn","ror":"https://ror.org/058kzsd48"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2995774564.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1528872935","https://openalex.org/W2010106791","https://openalex.org/W2950189064","https://openalex.org/W2048401959","https://openalex.org/W2106561717","https://openalex.org/W2102326671","https://openalex.org/W2070973599","https://openalex.org/W2092634984","https://openalex.org/W2121425277","https://openalex.org/W2068256165","https://openalex.org/W2081858615","https://openalex.org/W2023674741","https://openalex.org/W3195790439","https://openalex.org/W2032052270","https://openalex.org/W2105683922","https://openalex.org/W2792703944","https://openalex.org/W1988802668","https://openalex.org/W3197736549","https://openalex.org/W1996160615","https://openalex.org/W2133300496"],"abstract_inverted_index":{"In":[0],"dieser":[1,90],"Arbeit":[2],"untersuchen":[3],"wir":[4],"komplexit\u00e4tstheoretische":[5],"Aspekte":[6],"und":[7,150,206],"Algorithmen":[8,194],"mit":[9,183],"garantierter":[10],"Approximationsg\u00fcte":[11],"f\u00fcr":[12,92],"verschiedene":[13,93],"Probleme":[14,62,94],"der":[15,74,162,178,201,203,211],"geometrischen":[16],"Platzierung.":[17],"Der":[18],"Fokus":[19],"liegt":[20],"dabei":[21],"auf":[22,43],"dem":[23],"Fuzzy":[24,41,121,180],"k-Means":[25,42,122,181],"Problem,":[26],"welches":[27],"bisher":[28,192],"nicht":[29,124,140],"substantiell":[30],"theoretisch":[31],"untersucht":[32],"wurde.":[33],"Wir":[34,87,174],"zeigen,":[35],"dass":[36,89,100,116],"eine":[37,47,82,109,142,169,190],"Variante":[38],"von":[39,153,200,210],"Discrete":[40],"metrischen":[44],"R\u00e4umen,":[45],"sowie":[46],"hier":[48],"neu":[49],"definierte":[50],"Radiusvariante":[51],"dieses":[52],"Problems,":[53],"NP-schwer":[54],"sind.":[55,132],"Eine":[56],"beliebte":[57],"algorithmische":[58],"Herangehensweise":[59],"an":[60,213],"diese":[61],"ist":[63,205],"die":[64,148,207],"single-swap":[65,110],"Heuristik.":[66],"Dieser":[67,187],"lokale":[68],"Suchalgorithmus":[69],"tauscht":[70],"iterativ":[71],"einen":[72,78,176],"Repr\u00e4sentanten":[73],"aktuellen":[75],"L\u00f6sung":[76,84,172],"gegen":[77],"anderen":[79],"Kandidatenpunkt,":[80],"bis":[81,108],"stabile":[83],"gefunden":[85],"wird.":[86],"beweisen,":[88],"Algorithmus":[91,188],"streng":[95],"PLS-vollst\u00e4ndig":[96],"ist.":[97,216],"Das":[98],"hei\u00dft,":[99],"im":[101],"worst-case":[102],"exponentiell":[103],"viele":[104],"Iterationen":[105],"ben\u00f6tigt":[106],"werden,":[107],"Suche":[111],"terminiert.":[112],"Anschlie\u00dfend":[113],"zeigen":[114],"wir,":[115],"optimale":[117,138,171],"L\u00f6sungen":[118,139],"des":[119],"allgemeinen":[120],"Problems":[123],"durch":[125,141,147],"Radikale":[126],"\u00fcber":[127],"den":[128],"rationalen":[129],"Zahlen":[130,146],"l\u00f6sbar":[131],"Es":[133],"gibt":[134],"also":[135],"Instanzen,":[136],"deren":[137],"endliche":[143],"Verkettung":[144],"rationaler":[145],"Grundrechenarten":[149],"das":[151,164,179],"Ziehen":[152],"Wurzeln":[154],"dargestellt":[155],"werden":[156],"k\u00f6nnen.":[157],"Folglich":[158],"kann":[159],"jeder":[160],"Algorithmus,":[161,177],"versucht,":[163],"Problem":[165,182],"zu":[166],"l\u00f6sen,":[167],"h\u00f6chstens":[168],"approximativ":[170],"finden.":[173],"pr\u00e4sentieren":[175],"Faktor":[184],"(1+epsilon)":[185],"approximiert.":[186],"stellt":[189],"Verbesserung":[191],"bekannter":[193],"dar,":[195],"da":[196],"seine":[197],"Laufzeit":[198],"unabh\u00e4ngig":[199],"Gewichtung":[202],"Eingabepunkte":[204],"exponentielle":[208],"Abh\u00e4ngigkeit":[209],"Anzahl":[212],"Clustern":[214],"linear":[215]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}