{"id":"https://openalex.org/W3121185505","doi":"https://doi.org/10.1145/3543684","title":"Point-hyperplane Incidence Geometry and the Log-rank Conjecture","display_name":"Point-hyperplane Incidence Geometry and the Log-rank Conjecture","publication_year":2022,"publication_date":"2022-06-30","ids":{"openalex":"https://openalex.org/W3121185505","doi":"https://doi.org/10.1145/3543684","mag":"3121185505"},"language":"en","primary_location":{"id":"doi:10.1145/3543684","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3543684","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.57","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082108397","display_name":"Noah Singer","orcid":"https://orcid.org/0000-0002-0076-521X"},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Noah Singer","raw_affiliation_strings":["Harvard University, Cambridge, Massachusetts"],"affiliations":[{"raw_affiliation_string":"Harvard University, Cambridge, Massachusetts","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101519422","display_name":"Madhu Sudan","orcid":"https://orcid.org/0000-0003-3718-6489"},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Madhu Sudan","raw_affiliation_strings":["Harvard University, Cambridge, Massachusetts"],"affiliations":[{"raw_affiliation_string":"Harvard University, Cambridge, Massachusetts","institution_ids":["https://openalex.org/I2801851002"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082108397"],"corresponding_institution_ids":["https://openalex.org/I2801851002"],"apc_list":null,"apc_paid":null,"fwci":1.8372,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.8903912,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"14","issue":"2","first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"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":0.9994999766349792,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.9016236066818237},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8598321676254272},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.761483907699585},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7269682288169861},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5844647884368896},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.48090100288391113},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44749048352241516},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39081522822380066},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3108130693435669}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.9016236066818237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8598321676254272},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.761483907699585},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7269682288169861},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5844647884368896},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.48090100288391113},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44749048352241516},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39081522822380066},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3108130693435669},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3543684","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3543684","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"},{"id":"pmh:oai:drops-oai.dagstuhl.de:16065","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.57","pdf_url":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},{"id":"pmh:oai:arXiv.org:2101.09592","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.09592","pdf_url":"https://arxiv.org/pdf/2101.09592","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":null,"raw_type":"text"},{"id":"doi:10.4230/lipics.socg.2022.57","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2022.57","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:16065","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.57","pdf_url":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W176690618","https://openalex.org/W1495916036","https://openalex.org/W1551614270","https://openalex.org/W1664849218","https://openalex.org/W1965488421","https://openalex.org/W1986701615","https://openalex.org/W1994366967","https://openalex.org/W1997315904","https://openalex.org/W2002501531","https://openalex.org/W2024073594","https://openalex.org/W2028140545","https://openalex.org/W2043872822","https://openalex.org/W2045472305","https://openalex.org/W2047230132","https://openalex.org/W2050639196","https://openalex.org/W2053910492","https://openalex.org/W2069367490","https://openalex.org/W2083179104","https://openalex.org/W2115738326","https://openalex.org/W2145501841","https://openalex.org/W2161519549","https://openalex.org/W2166961358","https://openalex.org/W2175167577","https://openalex.org/W2282727044","https://openalex.org/W2962915177","https://openalex.org/W2963468679","https://openalex.org/W3000142391","https://openalex.org/W3003993007","https://openalex.org/W4211154544","https://openalex.org/W4239534271"],"related_works":["https://openalex.org/W2369655046","https://openalex.org/W2019467317","https://openalex.org/W1585519779","https://openalex.org/W1965515989","https://openalex.org/W4376167435","https://openalex.org/W2088737283","https://openalex.org/W1999587863","https://openalex.org/W4299565411","https://openalex.org/W2951225764","https://openalex.org/W3172879256"],"abstract_inverted_index":{"We":[0,12,130,163,204,243],"study":[1],"the":[2,6,14,51,54,62,72,77,138,141,170,174,177,185,200,210,316,332,346,358],"log-rank":[3,139,347],"conjecture":[4,92,134],"from":[5,150],"perspective":[7],"of":[8,30,50,56,61,71,116,144,169,179,202,212,216,249,283,285,319,334],"point-hyperplane":[9,78,193],"incidence":[10,79,194,231,268,292],"geometry.":[11],"formulate":[13],"following":[15],"conjecture:":[16],"Given":[17],"a":[18,41,58,68,85,114,148,257],"point":[19],"set":[20,321],"in":[21,53,67,110,124,192,225,315],"\u211d":[22],"d":[23,46,101,121,221,223,227,273,304],"that":[24,38,132,176],"is":[25,128,135,147,270],"covered":[26],"by":[27,184],"constant-sized":[28],"sets":[29,178],"parallel":[31,153,159,366],"hyperplanes,":[32],"there":[33],"exists":[34],"an":[35,166,206,246],"affine":[36],"subspace":[37],"accounts":[39],"for":[40,81,152,158,209,311,345,365,374],"large":[42,59,69,86],"(i.e.,":[43,199],"2":[44,119,220,254,301],"\u2013polylog(":[45,120],")":[47,48,122,224,305],"fraction":[49,60,70],"incidences,":[52],"sense":[55],"containing":[57,103],"points":[63],"and":[64,251,266,296,307,325],"being":[65],"contained":[66],"hyperplanes.":[73],"In":[74,349],"other":[75],"words,":[76],"graph":[80],"such":[82],"configurations":[83,290,368],"has":[84],"complete":[87,213,260,297,360],"bipartite":[88,214,261,298,361],"subgraph.":[89],"Alternatively,":[90],"our":[91,133,371],"may":[93,327],"be":[94,181],"interpreted":[95],"linear-algebraically":[96],"as":[97],"follows:":[98],"Any":[99],"rank-":[100],"matrix":[102],"at":[104],"most":[105],"O":[106],"(1)":[107,295],"distinct":[108],"entries":[109],"each":[111,126],"column":[112,127],"contains":[113],"submatrix":[115],"fractional":[117],"size":[118,363],",":[123,306],"which":[125,172,288,369],"constant.":[129],"prove":[131],"equivalent":[136],"to":[137,156,281],"conjecture;":[140],"crucial":[142],"ingredient":[143],"this":[145,312,354],"proof":[146],"reduction":[149],"bounds":[151,157,364,373],"k":[154,161],"-partitions":[155],"(":[160],"-1)-partitions.":[162],"also":[164,244],"introduce":[165],"(apparent)":[167],"strengthening":[168],"conjecture,":[171],"relaxes":[173],"requirements":[175],"hyperplanes":[180],"parallel.":[182],"Motivated":[183],"connections":[186],"above,":[187],"we":[188,276],"revisit":[189],"well-studied":[190],"questions":[191,310],"geometry":[195],"without":[196],"structural":[197],"assumptions":[198],"existence":[201,211],"partitions).":[203],"give":[205],"elementary":[207],"argument":[208],"subgraphs":[215,262],"density":[217,232,269,293,300],"\u03a9":[218,271,294],"(\u03b5":[219],"/":[222],"any":[226,351],"-dimensional":[228],"configuration":[229,258],"with":[230,291],"\u03b5,":[233],"qualitatively":[234],"matching":[235],"previous":[236],"results":[237,326],"proved":[238],"using":[239],"sophisticated":[240],"geometric":[241],"techniques.":[242],"improve":[245],"upper-bound":[247],"construction":[248],"Apfelbaum":[250],"Sharir":[252],"[":[253,342],"],":[255],"yielding":[256],"whose":[259,267],"are":[263],"exponentially":[264],"small":[265],"(1/\u221a":[272],").":[274],"Finally,":[275],"discuss":[277],"various":[278],"constructions":[279],"(due":[280],"others)":[282],"products":[284],"Boolean":[286],"matrices":[287],"yield":[289],"subgraph":[299,362],"-\u03a9":[302],"(\u221a":[303],"pose":[308],"several":[309],"special":[313],"case":[314],"alternative":[317],"language":[318],"extremal":[320],"combinatorics.":[322],"Our":[323],"framework":[324],"help":[328],"shed":[329],"light":[330],"on":[331,353],"difficulty":[333],"improving":[335],"Lovett\u2019s":[336],"\u00d5(\u221a":[337],"rank(":[338],"f":[339],"))":[340],"bound":[341,355],"20":[343],"]":[344],"conjecture.":[348],"particular,":[350],"improvement":[352],"would":[356],"imply":[357],"first":[359],"3-partitioned":[367],"beat":[370],"generic":[372],"unstructured":[375],"configurations.":[376]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2021-02-01T00:00:00"}
