{"id":"https://openalex.org/W7162509595","doi":"https://doi.org/10.4230/lipics.socg.2026.12","title":"Dynamic and Streaming Algorithms for Union Volume Estimation","display_name":"Dynamic and Streaming Algorithms for Union Volume Estimation","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7162509595","doi":"https://doi.org/10.4230/lipics.socg.2026.12"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25818","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.12","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.12/LIPIcs.SoCG.2026.12.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"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.12/LIPIcs.SoCG.2026.12.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136864384","display_name":"Sujoy Bhore","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Bhore, Sujoy","raw_affiliation_strings":["Indian Institute of Technology Bombay, Mumbai, India"],"raw_orcid":"https://orcid.org/0000-0003-0104-1659","affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044394587","display_name":"Karl Bringmann","orcid":"https://orcid.org/0000-0003-1356-5177"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bringmann, Karl","raw_affiliation_strings":["Saarland University and Max-Planck-Institute for Informatics, Saarbr\u00fccken, Germany"],"raw_orcid":"https://orcid.org/0000-0003-1356-5177","affiliations":[{"raw_affiliation_string":"Saarland University and Max-Planck-Institute for Informatics, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130565982","display_name":"Timothy M. Chan","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chan, Timothy M.","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, IL, USA"],"raw_orcid":"https://orcid.org/0000-0002-8093-0675","affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032845602","display_name":"Y Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Wang, Yanheng","raw_affiliation_strings":["Saarland University and Max-Planck-Institute for Informatics, Saarbr\u00fccken, Germany"],"raw_orcid":"https://orcid.org/0009-0007-4365-8899","affiliations":[{"raw_affiliation_string":"Saarland University and Max-Planck-Institute for Informatics, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]}]}],"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":0.62294264,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.6061000227928162,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.6061000227928162,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.06689999997615814,"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":0.05939999967813492,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/oracle","display_name":"Oracle","score":0.6129000186920166},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5656999945640564},{"id":"https://openalex.org/keywords/volume","display_name":"Volume (thermodynamics)","score":0.5146999955177307},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.5005000233650208},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.48080000281333923},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4537000060081482},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4255000054836273},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.40639999508857727},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3937999904155731}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6948000192642212},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.6129000186920166},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5656999945640564},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.5146999955177307},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.5005000233650208},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4724999964237213},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4255000054836273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.414000004529953},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.40639999508857727},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3937999904155731},{"id":"https://openalex.org/C102392041","wikidata":"https://www.wikidata.org/wiki/Q592860","display_name":"Sliding window protocol","level":3,"score":0.37560001015663147},{"id":"https://openalex.org/C2779804580","wikidata":"https://www.wikidata.org/wiki/Q102047","display_name":"Suffix","level":2,"score":0.3521000146865845},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.3418000042438507},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.33250001072883606},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C102408133","wikidata":"https://www.wikidata.org/wiki/Q5156350","display_name":"Competitive analysis","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C187166803","wikidata":"https://www.wikidata.org/wiki/Q2835831","display_name":"Streaming algorithm","level":3,"score":0.27709999680519104},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C86426650","wikidata":"https://www.wikidata.org/wiki/Q7452504","display_name":"Sequential estimation","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C192368570","wikidata":"https://www.wikidata.org/wiki/Q1789829","display_name":"Digital geometry","level":5,"score":0.2572000026702881},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:25818","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.12","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.12/LIPIcs.SoCG.2026.12.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.socg.2026.12","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.12","pdf_url":null,"source":null,"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:25818","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.12","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.12/LIPIcs.SoCG.2026.12.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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7162509595.pdf","grobid_xml":"https://content.openalex.org/works/W7162509595.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"union":[1,12,128,142],"volume":[2,9,54,129,143],"estimation":[3,130,144],"problem":[4,32],"asks":[5],"to":[6,78],"(1\u00b1\u03b5)-approximate":[7],"the":[8,11,53,102,132,146,159,180,199],"of":[10,13,50,55,91,125,155,218,221],"n":[14],"given":[15,69],"objects":[16,103,126],"X\u2081,\u2026,X_n":[17],"\u2282":[18],"\u211d^d.":[19],"In":[20,88,135],"their":[21],"seminal":[22],"work":[23],"in":[24,33,36,104,131,145,169,203,224],"1989,":[25],"Karp,":[26],"Luby,":[27],"and":[28,63,85,95,112,153,167,172,175,194,206,209,216,227,230],"Madras":[29],"solved":[30],"this":[31,115,136],"time":[34,74,109,174,208,229],"O(n/\u03b5\u00b2)":[35],"an":[37,163,190,212],"oracle":[38,133,147],"model":[39,148],"where":[40],"each":[41],"object":[42,111],"X_i":[43,66],"can":[44,116],"be":[45,79,117],"accessed":[46],"via":[47],"three":[48],"types":[49],"queries:":[51],"obtain":[52,158],"X_i,":[56,62],"sample":[57],"a":[58,68,120],"random":[59],"point":[60,70],"from":[61],"test":[64],"whether":[65],"contains":[67],"x.":[71],"This":[72],"running":[73],"was":[75],"recently":[76],"shown":[77],"optimal":[80],"[Bringmann,":[81],"Larsen,":[82],"Nusser,":[83],"Rotenberg,":[84],"Wang,":[86],"SoCG'25].":[87],"another":[89],"line":[90],"work,":[92],"Meel,":[93],"Vinodchandran,":[94],"Chakraborty":[96],"[PODS'21]":[97],"designed":[98],"algorithms":[99,140],"that":[100,149],"read":[101],"one":[105],"pass":[106],"using":[107],"polylogarithmic":[108,113,170,204,225],"per":[110],"space;":[114,210],"phrased":[118],"as":[119],"dynamic":[121,183],"algorithm":[122,164,191,213],"supporting":[123,165,192,214],"insertions":[124,152,166,193,215],"for":[127,141,186],"model.":[134],"paper,":[137],"we":[138],"study":[139],"support":[150],"both":[151],"deletions":[154,168,217],"objects.":[156],"We":[157],"following":[160],"results:":[161],"1)":[162],"update":[171,205,226],"query":[173,207,228],"linear":[176],"space":[177],"(this":[178],"is":[179],"first":[181],"such":[182],"algorithm,":[184],"even":[185],"2D":[187],"triangles);":[188],"2)":[189],"suffix":[195],"queries":[196],"(which":[197],"generalizes":[198],"sliding":[200],"window":[201],"setting)":[202],"3)":[211],"convex":[219],"bodies":[220],"constant":[222],"dimension":[223],"space.":[231]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-28T00:00:00"}
