{"id":"https://openalex.org/W4401422447","doi":"https://doi.org/10.1145/3677608","title":"Tight Bounds for Monotone Minimal Perfect Hashing","display_name":"Tight Bounds for Monotone Minimal Perfect Hashing","publication_year":2024,"publication_date":"2024-08-08","ids":{"openalex":"https://openalex.org/W4401422447","doi":"https://doi.org/10.1145/3677608"},"language":"en","primary_location":{"id":"doi:10.1145/3677608","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3677608","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3677608","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"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 Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3677608","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106358476","display_name":"Sepehr Assadi","orcid":"https://orcid.org/0000-0001-6482-6053"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA","US"],"is_corresponding":true,"raw_author_name":"Sepehr Assadi","raw_affiliation_strings":["University of Waterloo, Waterloo, ON, Canada","Rutgers University, USA"],"raw_orcid":"https://orcid.org/0000-0001-6482-6053","affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Rutgers University, USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087023890","display_name":"Mart\u0131\u0301n Farach-Colton","orcid":"https://orcid.org/0000-0003-3616-7788"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mart\u00edn Farach-Colton","raw_affiliation_strings":["New York University, Brooklyn, NY, USA","New York University, USA"],"raw_orcid":"https://orcid.org/0000-0003-3616-7788","affiliations":[{"raw_affiliation_string":"New York University, Brooklyn, NY, USA","institution_ids":["https://openalex.org/I57206974"]},{"raw_affiliation_string":"New York University, USA","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005111940","display_name":"William Kuszmaul","orcid":"https://orcid.org/0000-0002-3855-3036"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"William Kuszmaul","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA","Massachusetts Institute of Technology, USA"],"raw_orcid":"https://orcid.org/0000-0002-3855-3036","affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5106358476"],"corresponding_institution_ids":["https://openalex.org/I102322142","https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.324,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64213108,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"21","issue":"4","first_page":"1","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9976999759674072,"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"}},{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12029","display_name":"DNA and Biological Computing","score":0.954800009727478,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7470912337303162},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6961507797241211},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5810644626617432},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5400325655937195},{"id":"https://openalex.org/keywords/hash-function","display_name":"Hash function","score":0.5395449995994568},{"id":"https://openalex.org/keywords/perfect-hash-function","display_name":"Perfect hash function","score":0.5338920950889587},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.526674211025238},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4704129993915558},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.45946502685546875},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.446113646030426},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.426784873008728},{"id":"https://openalex.org/keywords/hash-table","display_name":"Hash table","score":0.1816801130771637},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1516839861869812},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14424249529838562}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7470912337303162},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6961507797241211},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5810644626617432},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5400325655937195},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.5395449995994568},{"id":"https://openalex.org/C87431388","wikidata":"https://www.wikidata.org/wiki/Q2070573","display_name":"Perfect hash function","level":4,"score":0.5338920950889587},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.526674211025238},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4704129993915558},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.45946502685546875},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.446113646030426},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.426784873008728},{"id":"https://openalex.org/C67388219","wikidata":"https://www.wikidata.org/wiki/Q207440","display_name":"Hash table","level":3,"score":0.1816801130771637},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1516839861869812},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14424249529838562},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3677608","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3677608","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3677608","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"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 Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3677608","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3677608","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3677608","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"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 Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7964149644","display_name":null,"funder_award_id":"FA8750-19-2-1000","funder_id":"https://openalex.org/F4320338294","funder_display_name":"Air Force Research Laboratory"}],"funders":[{"id":"https://openalex.org/F4320308782","display_name":"Hertz Foundation","ror":"https://ror.org/01ycgxf29"},{"id":"https://openalex.org/F4320338294","display_name":"Air Force Research Laboratory","ror":"https://ror.org/02e2egq70"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4401422447.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1561272249","https://openalex.org/W1969884330","https://openalex.org/W1988110322","https://openalex.org/W2015322433","https://openalex.org/W2053816258","https://openalex.org/W2068471245","https://openalex.org/W2069566112","https://openalex.org/W2074229180","https://openalex.org/W2077850713","https://openalex.org/W2088263428","https://openalex.org/W2095717436","https://openalex.org/W2164107415","https://openalex.org/W2889833303","https://openalex.org/W2999295646","https://openalex.org/W3010768629","https://openalex.org/W4250699352"],"related_works":["https://openalex.org/W2097286495","https://openalex.org/W2080388000","https://openalex.org/W2155123971","https://openalex.org/W1897694601","https://openalex.org/W1845395494","https://openalex.org/W62638829","https://openalex.org/W2083620925","https://openalex.org/W3131985603","https://openalex.org/W1551533237","https://openalex.org/W1987789009"],"abstract_inverted_index":{"The":[0,62,179],"monotone":[1,121],"minimal":[2,122],"perfect":[3,123],"hash":[4],"function":[5],"(MMPHF)":[6],"problem":[7,52,69,88],"is":[8,105,183,212],"the":[9,36,50,68,92,112,157,160,175,188,191,201,207],"following":[10,37],"indexing":[11],"problem.":[12],"Given":[13],"a":[14,22,30,132,153],"set":[15],"\\(S=\\{s_{1},\\ldots,s_{n}\\}\\)":[16],"of":[17,25,40,125,128,134,181,190,194,210],"\\(n\\)":[18,129],"distinct":[19],"keys":[20],"from":[21,131],"universe":[23,133],"\\(U\\)":[24],"size":[26,135,180],"\\(u\\)":[27,136],",":[28],"create":[29],"data":[31,115],"structure":[32,116],"\\(\\mathbf{D}\\)":[33,71,177,182],"that":[34,99,200],"answers":[35],"query:":[38],"\\(\\rm{{R\\small{ANK}}}(q)=\\begin{cases}\\text{rank":[39],"}q\\text{":[41],"in":[42,54,57,72,79],"}S&q\\in":[43],"S":[44],"\\\\":[45],"\\text{arbitrary":[46],"answer}&\\text{otherwise.}\\end{cases}\\)":[47],"Solutions":[48],"to":[49,89,97,141],"MMPHF":[51],"are":[53,159,169],"widespread":[55],"use":[56],"both":[58],"theory":[59],"and":[60,76,165],"practice.":[61],"best":[63],"upper":[64,94],"bound":[65,95,104,150],"known":[66],"for":[67,120],"encodes":[70],"\\(O(n\\log\\log\\log":[73],"u)\\)":[74,81],"bits":[75,140],"performs":[77],"queries":[78],"\\(O(\\log":[80],"time.":[82],"It":[83],"has":[84],"been":[85],"an":[86],"open":[87],"either":[90],"improve":[91],"space":[93],"or":[96,118],"show":[98,111,199],"this":[100,108],"somewhat":[101],"odd":[102],"looking":[103],"tight.":[106],"In":[107],"article,":[109],"we":[110,198],"latter:":[113],"any":[114,126],"(deterministic":[117],"randomized)":[119],"hashing":[124],"collection":[127],"elements":[130],"requires":[137],"\\(\\Omega(n\\cdot\\log\\log\\log{u})\\)":[138],"expected":[139],"answer":[142],"every":[143],"query":[144],"correctly.":[145],"We":[146],"achieve":[147],"our":[148],"lower":[149,185,213],"by":[151,187,215],"defining":[152],"graph":[154],"\\(\\mathbf{G}\\)":[155,195,211],"where":[156,166],"nodes":[158,168],"possible":[161],"\\({u\\choose":[162],"n}\\)":[163],"inputs":[164],"two":[167],"adjacent":[170],"if":[171],"they":[172],"cannot":[173],"share":[174],"same":[176],".":[178,196,218],"then":[184],"bounded":[186,214],"log":[189],"chromatic":[192,203,208],"number":[193,204],"Finally,":[197],"fractional":[202],"(and":[205],"hence":[206],"number)":[209],"\\(2^{\\Omega(n\\log\\log\\log":[216],"u)}\\)":[217]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}