{"id":"https://openalex.org/W3017783081","doi":"https://doi.org/10.1007/s00453-021-00887-8","title":"On Perturbation Resilience of Non-uniform k-Center","display_name":"On Perturbation Resilience of Non-uniform k-Center","publication_year":2021,"publication_date":"2021-10-28","ids":{"openalex":"https://openalex.org/W3017783081","doi":"https://doi.org/10.1007/s00453-021-00887-8","mag":"3017783081"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-021-00887-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-021-00887-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-021-00887-8.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-021-00887-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001388244","display_name":"Sayan Bandyapadhyay","orcid":"https://orcid.org/0000-0001-8875-0102"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Sayan Bandyapadhyay","raw_affiliation_strings":["Department of Informatics, University of Bergen, Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001388244"],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.4525,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65253437,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"84","issue":"1","first_page":"13","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9948999881744385,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9818000197410583,"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/mathematics","display_name":"Mathematics","score":0.7008981704711914},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6236276030540466},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4727260172367096},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.46982455253601074},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4293646514415741},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09741654992103577},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08882814645767212}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7008981704711914},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6236276030540466},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4727260172367096},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.46982455253601074},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4293646514415741},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09741654992103577},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08882814645767212}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1007/s00453-021-00887-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-021-00887-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-021-00887-8.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2004.12633","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.12633","pdf_url":"https://arxiv.org/pdf/2004.12633","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3017783081","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2004.12633.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:bora.uib.no:11250/2984315","is_oa":true,"landing_page_url":"https://hdl.handle.net/11250/2984315","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:drops-oai.dagstuhl.de:12634","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.31","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"InProceedings"},{"id":"pmh:oai:pubmedcentral.nih.gov:8786812","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8786812","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica","raw_type":"Text"},{"id":"doi:10.48550/arxiv.2004.12633","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2004.12633","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:3082916406","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2004.12633","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.4230/lipics.approx/random.2020.31","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.approx/random.2020.31","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":""}],"best_oa_location":{"id":"doi:10.1007/s00453-021-00887-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-021-00887-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-021-00887-8.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3748656914","display_name":null,"funder_award_id":"Norway","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"},{"id":"https://openalex.org/G7931603690","display_name":null,"funder_award_id":"MULTIVAL","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"}],"funders":[{"id":"https://openalex.org/F4320323078","display_name":"Universitetet i Bergen","ror":"https://ror.org/03zga2b32"},{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"},{"id":"https://openalex.org/F4320326507","display_name":"Haukeland\u00a0Universitetssjukehus","ror":"https://ror.org/03np4e098"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3017783081.pdf","grobid_xml":"https://content.openalex.org/works/W3017783081.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1503339058","https://openalex.org/W1558625102","https://openalex.org/W1927951443","https://openalex.org/W1966395945","https://openalex.org/W1973264045","https://openalex.org/W1976619117","https://openalex.org/W1990772655","https://openalex.org/W2015784652","https://openalex.org/W2016984055","https://openalex.org/W2018165630","https://openalex.org/W2029698681","https://openalex.org/W2043174865","https://openalex.org/W2059971059","https://openalex.org/W2073583237","https://openalex.org/W2119265025","https://openalex.org/W2166566648","https://openalex.org/W2225750372","https://openalex.org/W2258410023","https://openalex.org/W2289504059","https://openalex.org/W2565644440","https://openalex.org/W2626597900","https://openalex.org/W2739434859","https://openalex.org/W2807895386","https://openalex.org/W2884886133","https://openalex.org/W2885224664","https://openalex.org/W2890639290","https://openalex.org/W2949165676","https://openalex.org/W2949530173","https://openalex.org/W2952098125","https://openalex.org/W2963896776","https://openalex.org/W2964242853","https://openalex.org/W2964340118","https://openalex.org/W3162678658"],"related_works":["https://openalex.org/W3082916406","https://openalex.org/W2741133644","https://openalex.org/W2398977735","https://openalex.org/W2950656721","https://openalex.org/W2978794977","https://openalex.org/W1964537764","https://openalex.org/W2899019281","https://openalex.org/W2061324666","https://openalex.org/W1615210815","https://openalex.org/W2956137306","https://openalex.org/W2906838315","https://openalex.org/W2020505980","https://openalex.org/W3035118655","https://openalex.org/W1973652906","https://openalex.org/W2950821282","https://openalex.org/W2574098572","https://openalex.org/W2949591167","https://openalex.org/W3184813396","https://openalex.org/W3135887889","https://openalex.org/W2143160814"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Non-Uniform":[2],"k":[3,28,92,184],"-center":[4,29],"(NUkC)":[5],"problem":[6,150,223,243],"has":[7],"recently":[8],"been":[9],"formulated":[10],"by":[11,230],"Chakrabarty":[12],"et":[13],"al.":[14],"[ICALP,":[15],"2016;":[16],"ACM":[17],"Trans":[18],"Algorithms":[19],"16(4):46:1\u201346:19,":[20],"2020]":[21],"as":[22],"a":[23,35,42,174,181,210,264],"generalization":[24],"of":[25,37,98,135,142,213],"the":[26,75,80,96,140,143,149,169,194,198,221,242,252,277,299],"classical":[27],"clustering":[30],"problem.":[31,300],"In":[32,216,280],"NUkC,":[33],"given":[34],"set":[36,212],"n":[38],"points":[39,97,134],"P":[40,99,136],"in":[41,139,165,193,276],"metric":[43],"space":[44],"and":[45,89,232],"non-negative":[46],"numbers":[47],"$$r_1,":[48],"r_2,":[49],"\\ldots":[50],",":[51,74,130],"r_k$$":[52],"<mml:math":[53,85,105,120,154,200,254],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[54,86,106,121,155,201,255],"<mml:mrow>":[55,107,122],"<mml:msub>":[56,61,68,110,202,256],"<mml:mi>r</mml:mi>":[57,62,69,111,203,257],"<mml:mn>1</mml:mn>":[58,123],"</mml:msub>":[59,64,71,113,205,259],"<mml:mo>,</mml:mo>":[60,65,67],"<mml:mn>2</mml:mn>":[63],"<mml:mo>\u2026</mml:mo>":[66],"<mml:mi>k</mml:mi>":[70,127],"</mml:mrow>":[72,114,128],"</mml:math>":[73,88,115,129,157,206,260],"goal":[76],"is":[77,151,190,247],"to":[78,90,159,209,263,293],"find":[79,294],"minimum":[81],"dilation":[82],"$$\\alpha":[83,102],"$$":[84],"<mml:mi>\u03b1</mml:mi>":[87,108],"choose":[91],"balls":[93],"centered":[94],"at":[95],"with":[100,287],"radius":[101],"\\cdot":[103],"r_i$$":[104],"<mml:mo>\u00b7</mml:mo>":[109],"<mml:mi>i</mml:mi>":[112,125,204,258],"for":[116,298],"$$1\\le":[117],"i\\le":[118],"k$$":[119],"<mml:mo>\u2264</mml:mo>":[124,126],"such":[131],"that":[132,148,179,241,270,285],"all":[133],"are":[137],"contained":[138],"union":[141],"chosen":[144],"balls.":[145,185],"They":[146],"showed":[147],"$$\\mathsf":[152],"{NP}$$":[153],"<mml:mi>NP</mml:mi>":[156],"-hard":[158],"approximate":[160],"within":[161],"any":[162,295],"factor":[163],"even":[164,192,286],"tree":[166],"metrics.":[167],"On":[168],"other":[170],"hand,":[171],"they":[172],"designed":[173],"\u201cbi-criteria\u201d":[175],"constant":[176,182],"approximation":[177,189,297],"algorithm":[178],"uses":[180],"times":[183],"Surprisingly,":[186],"no":[187],"true":[188],"known":[191],"special":[195],"case":[196],"when":[197,251],"$$r_i$$":[199,253],"\u2019s":[207,261],"belong":[208,262],"fixed":[211],"size":[214],"3.":[215],"this":[217],"paper,":[218],"we":[219,268],"study":[220],"NUkC":[222],"under":[224,244],"perturbation":[225,271,288],"resilience,":[226],"which":[227],"was":[228],"introduced":[229],"Bilu":[231],"Linial":[233],"(Comb":[234],"Probab":[235],"Comput":[236],"21(5):643\u2013660,":[237],"2012).":[238],"We":[239],"show":[240,269],"2-perturbation":[245],"resilience":[246,272,289],"polynomial":[248],"time":[249],"solvable":[250],"constant-sized":[265],"set.":[266],"However,":[267],"does":[273],"not":[274],"help":[275],"general":[278],"case.":[279],"particular,":[281],"our":[282],"findings":[283],"imply":[284],"one":[290],"cannot":[291],"hope":[292],"\u201cgood\u201d":[296]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
