{"id":"https://openalex.org/W4414754973","doi":"https://doi.org/10.4230/lipics.approx/random.2025.8","title":"Multipass Linear Sketches for Geometric LP-Type Problems","display_name":"Multipass Linear Sketches for Geometric LP-Type Problems","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4414754973","doi":"https://doi.org/10.4230/lipics.approx/random.2025.8"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2507.11484","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.11484","pdf_url":"https://arxiv.org/pdf/2507.11484","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},"type":"preprint","indexed_in":["arxiv","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2507.11484","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119817907","display_name":"N. Efe \u00c7ekirge","orcid":null},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"\u00c7ekirge, N. Efe","raw_affiliation_strings":["Department of Computer Science, Dartmouth College, Hanover, NH, USA"],"raw_orcid":"https://orcid.org/0009-0007-6531-7593","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Dartmouth College, Hanover, NH, USA","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055624394","display_name":"William O. Gay","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":"Gay, William","raw_affiliation_strings":["Grainger College of Engineering, University of Illinois, Urbana-Champaign, IL, USA"],"raw_orcid":"https://orcid.org/0009-0007-7912-5189","affiliations":[{"raw_affiliation_string":"Grainger College of Engineering, University of Illinois, Urbana-Champaign, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102861589","display_name":"David P. Woodruff","orcid":"https://orcid.org/0000-0002-2158-1380"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Woodruff, David P.","raw_affiliation_strings":["Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0000-0002-2158-1380","affiliations":[{"raw_affiliation_string":"Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9958999752998352,"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":0.9958999752998352,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.7006000280380249},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.6241000294685364},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5648000240325928},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.5131000280380249},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.49810001254081726},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.49160000681877136},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.48989999294281006},{"id":"https://openalex.org/keywords/linear-space","display_name":"Linear space","score":0.40950000286102295},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.40059998631477356},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.36559998989105225}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7006000280380249},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.6241000294685364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5670999884605408},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5648000240325928},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.5131000280380249},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.49810001254081726},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.49160000681877136},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.48989999294281006},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4325999915599823},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.40950000286102295},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.36559998989105225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3506999909877777},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C75684735","wikidata":"https://www.wikidata.org/wiki/Q858810","display_name":"Big data","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3303000032901764},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.3165000081062317},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3093000054359436},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C20729856","wikidata":"https://www.wikidata.org/wiki/Q2078279","display_name":"Geometric programming","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.29249998927116394},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C52486349","wikidata":"https://www.wikidata.org/wiki/Q17006040","display_name":"Criss-cross algorithm","level":4,"score":0.25769999623298645},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.25360000133514404},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.2515999972820282},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2507.11484","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.11484","pdf_url":"https://arxiv.org/pdf/2507.11484","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"doi:10.48550/arxiv.2507.11484","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.11484","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.4230/lipics.approx/random.2025.8","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.approx/random.2025.8","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:arXiv.org:2507.11484","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.11484","pdf_url":"https://arxiv.org/pdf/2507.11484","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"LP-type":[0,43,106],"problems":[1,44,107],"such":[2,34],"as":[3,35],"the":[4,62,156],"Minimum":[5],"Enclosing":[6],"Ball":[7],"(MEB),":[8],"Linear":[9,14],"Support":[10],"Vector":[11],"Machine":[12],"(SVM),":[13],"Programming":[15,19],"(LP),":[16],"and":[17,38,48,111,129,161],"Semidefinite":[18],"(SDP)":[20],"are":[21],"fundamental":[22],"combinatorial":[23,110],"optimization":[24],"problems,":[25,164],"with":[26,58,66,84],"many":[27],"important":[28],"applications":[29,33],"in":[30,45,92,127,131,136],"machine":[31],"learning":[32],"classification,":[36],"bioinformatics,":[37],"noisy":[39],"learning.":[40],"We":[41,141],"study":[42],"several":[46],"streaming":[47],"distributed":[49],"big":[50],"data":[51],"models,":[52],"giving":[53],"\u03b5-approximation":[54],"linear":[55,162],"sketching":[56],"algorithms":[57],"a":[59],"focus":[60],"on":[61],"high":[63],"accuracy":[64],"regime":[65],"low":[67],"dimensionality":[68],"d,":[69],"that":[70],"is,":[71],"when":[72],"d":[73,100,119,128],"<":[74],"(1/\u03b5)^0.999.":[75],"Our":[76],"main":[77],"result":[78],"is":[79],"an":[80],"O(ds)":[81],"pass":[82],"algorithm":[83,154],"O(s(\u221ad/\u03b5)^{3d/s})":[85],"\u22c5":[86],"poly(d,":[87],"log":[88,101,120],"(1/\u03b5))":[89],"space":[90,124],"complexity":[91,125],"words,":[93],"for":[94,151],"any":[95,152],"parameter":[96],"s":[97,117],"\u2208":[98],"[1,":[99],"(1/\u03b5)],":[102],"to":[103],"solve":[104],"\u03b5-approximate":[105],"of":[108,149],"O(d)":[109],"VC":[112],"dimension.":[113],"Notably,":[114],"by":[115,145],"taking":[116],"=":[118],"(1/\u03b5),":[121],"we":[122],"achieve":[123],"polynomial":[126],"polylogarithmic":[130],"1/\u03b5,":[132],"presenting":[133],"exponential":[134],"improvements":[135],"1/\u03b5":[137],"over":[138],"current":[139],"algorithms.":[140],"complement":[142],"our":[143,167],"results":[144],"showing":[146],"lower":[147],"bounds":[148],"(1/\u03b5)^\u03a9(d)":[150],"1-pass":[153],"solving":[155],"(1":[157],"+":[158],"\u03b5)-approximation":[159],"MEB":[160],"SVM":[163],"further":[165],"motivating":[166],"multi-pass":[168],"approach.":[169]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-02T00:00:00"}
