{"id":"https://openalex.org/W7160496076","doi":"https://doi.org/10.48550/arxiv.2605.04798","title":"Online Orthogonal Vectors Revisited","display_name":"Online Orthogonal Vectors Revisited","publication_year":2026,"publication_date":"2026-05-06","ids":{"openalex":"https://openalex.org/W7160496076","doi":"https://doi.org/10.48550/arxiv.2605.04798"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.04798","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04798","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.04798","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051473853","display_name":"Karthik Gajulapalli","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gajulapalli, Karthik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062090877","display_name":"Alexander Golovnev","orcid":"https://orcid.org/0000-0002-7847-1027"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Golovnev, Alexander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122301211","display_name":"Samuel King","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"King, Samuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059723204","display_name":"Sidhant Saraogi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saraogi, Sidhant","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.5838000178337097,"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":0.5838000178337097,"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/T12288","display_name":"Optimization and Search Problems","score":0.18719999492168427,"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/T10237","display_name":"Cryptography and Data Security","score":0.06379999965429306,"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/data-structure","display_name":"Data structure","score":0.616100013256073},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.5299000144004822},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5267999768257141},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4359999895095825},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4153999984264374},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.3662000000476837},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.36500000953674316},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3427000045776367},{"id":"https://openalex.org/keywords/linear-space","display_name":"Linear space","score":0.3246000111103058}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6438999772071838},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.616100013256073},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5525000095367432},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.5299000144004822},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5267999768257141},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45829999446868896},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4350999891757965},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4153999984264374},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3662000000476837},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.36500000953674316},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3427000045776367},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3052999973297119},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.30390000343322754},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C12439846","wikidata":"https://www.wikidata.org/wiki/Q4809258","display_name":"Database theory","level":3,"score":0.28060001134872437},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.04798","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04798","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"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.04798","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04798","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":false,"raw_source_name":null,"raw_type":"Preprint"},"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":{"We":[0,57,152,212],"prove":[1,171,214],"new":[2,60],"upper":[3],"and":[4,24,41,104,129,149,208],"lower":[5,176,193,216],"bounds":[6,177,194,217],"for":[7,64,178,218],"the":[8,53,78,81,98,109,113,121,163,223],"Online":[9],"Orthogonal":[10,146,205],"Vectors":[11],"Problem":[12],"($\\mathsf{OnlineOV}_{n,d}$).":[13],"In":[14,66],"this":[15],"problem,":[16],"a":[17,26,37,59,118,139,154],"preprocessing":[18,221],"algorithm":[19,34,85],"receives":[20,36],"$n$":[21],"vectors":[22,55],"$x_1,\\ldots,x_n\\in\\{0,1\\}^d$":[23],"constructs":[25],"data":[27,62,75,134,181],"structure":[28,63,76,135,182],"of":[29,52,80,117,123,141],"size":[30],"$S$.":[31],"A":[32],"query":[33,38,185],"subsequently":[35],"vector":[39],"$q\\in\\{0,1\\}^d$":[40],"in":[42,92],"time":[43,186],"$T$":[44],"decides":[45],"whether":[46],"$q$":[47],"is":[48],"orthogonal":[49],"to":[50,87,138,158,196],"any":[51,179],"input":[54],"$x_i$.":[56],"design":[58,159],"deterministic":[61,115],"$\\mathsf{OnlineOV}_{n,d}$.":[65],"low":[67],"dimensions":[68,94],"($d":[69],"=":[70],"c":[71],"\\log":[72],"n$),":[73],"our":[74,160],"matches":[77],"performance":[79],"best":[82],"known":[83],"randomized":[84],"due":[86],"Chan":[88],"[SoCG":[89],"2017].":[90,132],"Furthermore,":[91],"moderate":[93],"($d=n^{\\varepsilon}$),":[95],"we":[96,111,169],"give":[97,112],"first":[99,114],"improvement":[100],"since":[101],"Charikar,":[102],"Indyk":[103],"Panigrahy":[105],"[ICALP":[106],"2002].":[107],"Along":[108],"way,":[110],"refutation":[116],"conjecture":[119],"on":[120],"hardness":[122],"$\\mathsf{OnlineOV}$":[124,180],"posed":[125],"by":[126],"Goldstein,":[127],"Lewenstein":[128],"Porat":[130],"[ISAAC":[131],"This":[133],"also":[136,170,213],"extends":[137],"number":[140],"problems,":[142,199],"including":[143,200],"Partial":[144,203],"Match,":[145,204],"Range":[147,206],"Search,":[148,207],"DNF":[150],"Evaluation.":[151],"use":[153],"novel":[155],"structure-versus-randomness":[156],"decomposition":[157],"algorithm.":[161],"Under":[162],"Non-Uniform":[164,224],"Strong":[165],"Exponential":[166],"Time":[167],"Hypothesis,":[168],"arbitrarily":[172],"large":[173],"polynomial":[174],"space":[175],"with":[183,188,220],"sublinear":[184],"even":[187],"computationally":[189],"unbounded":[190],"preprocessing.":[191],"These":[192],"extend":[195],"several":[197],"other":[198],"Polynomial":[201],"Evaluation,":[202],"Approximate":[209],"Nearest":[210],"Neighbors.":[211],"similar":[215],"$\\mathsf{3-SUM}$":[219],"under":[222],"Hamiltonian":[225],"Path":[226],"Conjecture.":[227]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-08T00:00:00"}