{"id":"https://openalex.org/W7166848401","doi":"https://doi.org/10.4230/lipics.icalp.2026.70","title":"Incremental (k, z)-Clustering on Graphs","display_name":"Incremental (k, z)-Clustering on Graphs","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7166848401","doi":"https://doi.org/10.4230/lipics.icalp.2026.70"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26459","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.70","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.70/LIPIcs.ICALP.2026.70.pdf","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":null,"raw_type":"InProceedings"},"type":"article","indexed_in":["datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.70/LIPIcs.ICALP.2026.70.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041514469","display_name":"Emilio Cruciani","orcid":"https://orcid.org/0000-0002-4744-5635"},"institutions":[{"id":"https://openalex.org/I4210099865","display_name":"European University of Rome","ror":"https://ror.org/011at3t25","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210099865"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Cruciani, Emilio","raw_affiliation_strings":["European University of Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-4744-5635","affiliations":[{"raw_affiliation_string":"European University of Rome, Italy","institution_ids":["https://openalex.org/I4210099865"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053481668","display_name":"Sebastian Forster","orcid":"https://orcid.org/0000-0002-2191-3381"},"institutions":[{"id":"https://openalex.org/I182212641","display_name":"University of Salzburg","ror":"https://ror.org/05gs8cd61","country_code":"AT","type":"education","lineage":["https://openalex.org/I182212641"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Forster, Sebastian","raw_affiliation_strings":["Department of Computer Science, University of Salzburg, Austria"],"raw_orcid":"https://orcid.org/0000-0002-2191-3381","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Salzburg, Austria","institution_ids":["https://openalex.org/I182212641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073557610","display_name":"Antonis Skarlatos","orcid":"https://orcid.org/0000-0002-7623-9419"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Skarlatos, Antonis","raw_affiliation_strings":["Department of Computer Science, University of Warwick, Coventry, UK"],"raw_orcid":"https://orcid.org/0000-0002-7623-9419","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Warwick, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.71719906,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T11502","display_name":"Facility Location and Emergency Management","score":0.7010999917984009,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.7010999917984009,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.034299999475479126,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.025299999862909317,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.6554999947547913},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5230000019073486},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5127999782562256},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.48590001463890076},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4120999872684479},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4043000042438507},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.3628000020980835}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6554999947547913},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.617900013923645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5507000088691711},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5230000019073486},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5127999782562256},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.48590001463890076},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4162999987602234},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4120999872684479},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3628000020980835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.349700003862381},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3345000147819519},{"id":"https://openalex.org/C99580578","wikidata":"https://www.wikidata.org/wiki/Q5319002","display_name":"Dynamic problem","level":2,"score":0.32359999418258667},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30809998512268066},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.28360000252723694},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2734000086784363},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.2702000141143799},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:26459","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.70","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.70/LIPIcs.ICALP.2026.70.pdf","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":null,"raw_type":"InProceedings"},{"id":"doi:10.4230/lipics.icalp.2026.70","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.icalp.2026.70","pdf_url":null,"source":{"id":"https://openalex.org/S4393917817","display_name":"Leibniz international proceedings in informatics","issn_l":"1868-8969","issn":["1868-8969"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26459","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.70","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.70/LIPIcs.ICALP.2026.70.pdf","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":null,"raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7166848401.pdf","grobid_xml":"https://content.openalex.org/works/W7166848401.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Given":[0],"a":[1,5,134,160,220,231,235,241,285,294,358,372,378,393,399],"weighted":[2,380],"undirected":[3],"graph,":[4],"number":[6],"of":[7,34,42,197,215,245,269,276,290,298,301,317,333,363],"clusters":[8],"k,":[9],"and":[10,58,77,101,105,109,131,159,190,274,324],"an":[11,84,256,265,314],"exponent":[12],"z,":[13],"the":[14,17,32,35,39,52,66,69,78,90,114,146,195,207,212,280,302,318,340,352,367,384],"goal":[15,79],"in":[16,89,122,234,342],"(k,":[18,86,116,223],"z)-clustering":[19,87,117,224],"problem":[20,50,118],"on":[21,183,377],"graphs":[22,184],"is":[23,71,80,154,255,313,338],"to":[24,38,45,73,81,138,156,175,194,329,348],"select":[25],"k":[26],"vertices":[27],"as":[28],"centers":[29],"that":[30,226,339,360],"minimize":[31],"sum":[33],"distances":[36,158,167],"raised":[37],"power":[40],"z":[41],"each":[43],"vertex":[44],"its":[46],"closest":[47],"center.":[48],"This":[49,141,310],"includes":[51],"well-known":[53],"k-median":[54],"(z":[55,60],"=":[56,61],"1)":[57],"k-means":[59],"2)":[62],"clustering":[63],"problems.":[64],"In":[65,279,366],"dynamic":[67,115,147,179,208,379,394],"setting,":[68,149],"graph":[70,148,236],"subject":[72],"adversarial":[74,128,307],"edge":[75,162,238,308],"updates,":[76],"maintain":[82,284,371],"explicitly":[83],"exact":[85],"solution":[88,289,376],"induced":[91,382],"shortest-path":[92],"metric.":[93],"Prior":[94],"works":[95],"by":[96,106,322,383],"Bhattacharya,":[97,107],"Costa,":[98,108],"Garg,":[99],"Lattanzi,":[100],"Parotsidis":[102],"[FOCS":[103],"2024]":[104],"Farokhnejad":[110],"[STOC":[111],"2025]":[112],"consider":[113],"for":[119,206],"point":[120,129],"sets":[121],"metric":[123],"spaces.":[124],"These":[125],"algorithms":[126,182],"support":[127],"insertions":[130,239],"deletions":[132],"under":[133],"model":[135,142],"with":[136,228,240,293,398],"access":[137,153],"pairwise":[139,157],"distances.":[140],"differs":[143],"significantly":[144],"from":[145],"where":[150,251],"no":[151,200],"oracle":[152],"given":[155],"single":[161],"update":[163,243,267,296],"can":[164,345],"affect":[165],"many":[166],"-":[168,357],"making":[169],"these":[170],"approaches":[171],"inefficient":[172],"when":[173],"applied":[174],"graphs.":[176,331],"While":[177],"efficient":[178],"k-center":[180],"approximation":[181,233,320,353],"exist":[185],"[Cruciani,":[186],"Forster,":[187],"Goranci,":[188],"Nazari,":[189],"Skarlatos,":[191],"SODA":[192],"2024],":[193],"best":[196],"our":[198,334],"knowledge,":[199],"prior":[201],"work":[202],"provides":[203],"similar":[204],"results":[205,337],"(k,z)-clustering":[209,375,401],"problem.":[210],"As":[211],"main":[213],"result":[214],"this":[216,389],"paper,":[217],"we":[218,283,370,391],"develop":[219],"randomized":[221],"incremental":[222,261,330],"algorithm":[225,262,321,344,396],"maintains":[227],"high":[229],"probability":[230],"constant-factor":[232,286,373],"undergoing":[237],"total":[242,295],"time":[244,268,297],"\u00d5(k":[246,270],"m^{1+o(1)}":[247,299],"+":[248,272],"k^{1+1/(\u03bb)}":[249],"m),":[250],"\u03bb":[252],"\u2265":[253],"1":[254],"arbitrary":[257],"fixed":[258],"constant.":[259],"Our":[260],"also":[263],"achieves":[264],"amortized":[266],"n^o(1)":[271],"k^{1+1/(\u03bb)})":[273],"consists":[275],"two":[277],"stages.":[278],"first":[281,311],"stage,":[282,369],"bicriteria":[287,319,385],"approximate":[288,374,386],"size":[291],"O\u0303(k)":[292],"(independent":[300],"parameter":[303],"k)":[304],"over":[305],"all":[306],"insertions.":[309],"stage":[312],"intricate":[315],"adaptation":[316],"Mettu":[323],"Plaxton":[325],"[Machine":[326],"Learning":[327],"2004]":[328],"One":[332],"key":[335],"technical":[336],"radii":[341],"their":[343],"be":[346,349,362],"assumed":[347],"non-decreasing":[350],"while":[351],"ratio":[354],"remains":[355],"constant":[356],"property":[359],"may":[361],"independent":[364],"interest.":[365],"second":[368],"instance":[381],"solution.":[387],"For":[388],"subproblem,":[390],"employ":[392],"spanner":[395],"together":[397],"static":[400],"algorithm.":[402]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2026-07-02T00:00:00"}