{"id":"https://openalex.org/W4362656067","doi":"https://doi.org/10.48550/arxiv.2304.01889","title":"Chasing Positive Bodies","display_name":"Chasing Positive Bodies","publication_year":2023,"publication_date":"2023-04-04","ids":{"openalex":"https://openalex.org/W4362656067","doi":"https://doi.org/10.48550/arxiv.2304.01889"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2304.01889","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.01889","pdf_url":"https://arxiv.org/pdf/2304.01889","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":"","raw_type":null},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2304.01889","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103251160","display_name":"Sayan Bhattacharya","orcid":"https://orcid.org/0000-0003-1612-0296"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bhattacharya, Sayan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002590915","display_name":"Niv Buchbinder","orcid":"https://orcid.org/0000-0002-7014-8954"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Buchbinder, Niv","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058909632","display_name":"Roie Levin","orcid":"https://orcid.org/0000-0003-2907-7186"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Levin, Roie","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5010547647","display_name":"Thatchaphol Saranurak","orcid":"https://orcid.org/0000-0001-8386-7168"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saranurak, Thatchaphol","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5103251160"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T12288","display_name":"Optimization and Search Problems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11502","display_name":"Facility Location and Emergency Management","score":0.9819999933242798,"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/T12137","display_name":"Economic theories and models","score":0.9514999985694885,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7519554495811462},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7429459095001221},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6173666715621948},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.570141077041626},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.5157275795936584},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5067632794380188},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.48922228813171387},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.45655930042266846},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.45608991384506226},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4349600076675415},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3606792390346527},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34702932834625244},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08174294233322144}],"concepts":[{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7519554495811462},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7429459095001221},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6173666715621948},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.570141077041626},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5157275795936584},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5067632794380188},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.48922228813171387},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.45655930042266846},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.45608991384506226},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4349600076675415},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3606792390346527},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34702932834625244},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08174294233322144},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2304.01889","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.01889","pdf_url":"https://arxiv.org/pdf/2304.01889","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":"","raw_type":null},{"id":"doi:10.48550/arxiv.2304.01889","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2304.01889","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2304.01889","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2304.01889","pdf_url":"https://arxiv.org/pdf/2304.01889","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":"","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2213600020","display_name":null,"funder_award_id":"2238138","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3330119427","display_name":null,"funder_award_id":"EPSRC","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3947296455","display_name":"Theory and Applications of Dynamic Algorithms","funder_award_id":"EP/S03353X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3103325625","https://openalex.org/W1486898455","https://openalex.org/W3090727460","https://openalex.org/W4306313719","https://openalex.org/W2041905724","https://openalex.org/W2991463004","https://openalex.org/W2088588293","https://openalex.org/W4311726894","https://openalex.org/W374487401","https://openalex.org/W2024436902"],"abstract_inverted_index":{"We":[0,92,148],"study":[1],"the":[2,28,49,69,104,118,159,169,179,200,206],"problem":[3,55],"of":[4,13,53,72,108,121,181,202],"chasing":[5,143],"positive":[6],"bodies":[7,14],"in":[8,76,137,205],"$\\ell_1$:":[9],"given":[10],"a":[11,34,61,195],"sequence":[12],"$K_{t}=\\{x^{t}\\in\\mathbb{R}_{+}^{n}\\mid":[15],"C^{t}x^{t}\\geq":[16],"1,P^{t}x^{t}\\leq":[17],"1\\}$":[18],"revealed":[19],"online,":[20],"where":[21,101],"$C^{t}$":[22],"and":[23,66,90,114],"$P^{t}$":[24],"are":[25],"nonnegative":[26],"matrices,":[27],"goal":[29],"is":[30,45,103,130,145,176,194],"to":[31,139,152,157,190],"(approximately)":[32],"maintain":[33],"point":[35],"$x_t":[36],"\\in":[37],"K_t$":[38],"such":[39,79],"that":[40,56],"$\\sum_t":[41],"\\|x_t":[42],"-":[43],"x_{t-1}\\|_1$":[44],"minimized.":[46],"This":[47,112,193],"captures":[48],"fully-dynamic":[50],"low-recourse":[51],"variant":[52],"any":[54,109],"can":[57],"be":[58],"expressed":[59],"as":[60,80],"mixed":[62],"packing-covering":[63],"linear":[64],"program":[65],"thus":[67],"also":[68,149],"fractional":[70],"version":[71],"many":[73],"central":[74],"problems":[75,171],"dynamic":[77,162,207],"algorithms":[78,163,208],"set":[81],"cover,":[82],"load":[83],"balancing,":[84],"hyperedge":[85],"orientation,":[86],"minimum":[87],"spanning":[88],"tree,":[89],"matching.":[91],"give":[93],"an":[94],"$O(\\log":[95],"d)$-competitive":[96],"algorithm":[97,129,184],"for":[98,124,167],"this":[99],"problem,":[100],"$d$":[102],"maximum":[105],"row":[106],"sparsity":[107],"matrix":[110],"$C^t$.":[111],"bypasses":[113],"improves":[115],"exponentially":[116],"over":[117],"lower":[119],"bound":[120],"$\\sqrt{n}$":[122],"known":[123],"general":[125,140],"convex":[126,141],"bodies.":[127],"Our":[128],"based":[131],"on":[132,185],"iterated":[133],"information":[134],"projections,":[135],"and,":[136],"contrast":[138],"body":[142],"algorithms,":[144],"entirely":[146],"memoryless.":[147],"show":[150],"how":[151],"round":[153],"our":[154],"solution":[155],"dynamically":[156],"obtain":[158],"first":[160],"fully":[161],"with":[164],"competitive":[165],"recourse":[166,175,180,204],"all":[168],"stated":[170],"above;":[172],"i.e.":[173],"their":[174],"less":[177],"than":[178,199],"every":[182,186],"other":[183],"update":[187],"sequence,":[188],"up":[189],"polylogarithmic":[191],"factors.":[192],"significantly":[196],"stronger":[197],"notion":[198,201],"absolute":[203],"literature.":[209]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
