{"id":"https://openalex.org/W7148876176","doi":"https://doi.org/10.48550/arxiv.2604.01307","title":"Space-Efficient Text Indexing with Mismatches using Function Inversion","display_name":"Space-Efficient Text Indexing with Mismatches using Function Inversion","publication_year":2026,"publication_date":"2026-04-01","ids":{"openalex":"https://openalex.org/W7148876176","doi":"https://doi.org/10.48550/arxiv.2604.01307"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.01307","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01307","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.01307","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132851106","display_name":"Jackson Bibbens","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bibbens, Jackson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038001587","display_name":"Levi Borevitz","orcid":"https://orcid.org/0009-0008-1725-6316"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Borevitz, Levi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006653893","display_name":"Samuel McCauley","orcid":"https://orcid.org/0000-0001-8196-9662"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"McCauley, Samuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"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/T11269","display_name":"Algorithms and Data Compression","score":0.964900016784668,"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":0.964900016784668,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.010400000028312206,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.005100000184029341,"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/substring","display_name":"Substring","score":0.6531999707221985},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.5213000178337097},{"id":"https://openalex.org/keywords/search-engine-indexing","display_name":"Search engine indexing","score":0.5131000280380249},{"id":"https://openalex.org/keywords/range-query","display_name":"Range query (database)","score":0.5066999793052673},{"id":"https://openalex.org/keywords/linear-space","display_name":"Linear space","score":0.5062999725341797},{"id":"https://openalex.org/keywords/query-optimization","display_name":"Query optimization","score":0.5016999840736389},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4560000002384186},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4097999930381775},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.38429999351501465}],"concepts":[{"id":"https://openalex.org/C182407805","wikidata":"https://www.wikidata.org/wiki/Q2626534","display_name":"Substring","level":3,"score":0.6531999707221985},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.5213000178337097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5138999819755554},{"id":"https://openalex.org/C75165309","wikidata":"https://www.wikidata.org/wiki/Q2258979","display_name":"Search engine indexing","level":2,"score":0.5131000280380249},{"id":"https://openalex.org/C136736807","wikidata":"https://www.wikidata.org/wiki/Q818943","display_name":"Range query (database)","level":5,"score":0.5066999793052673},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.5062999725341797},{"id":"https://openalex.org/C157692150","wikidata":"https://www.wikidata.org/wiki/Q2919848","display_name":"Query optimization","level":2,"score":0.5016999840736389},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4560000002384186},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4196999967098236},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4097999930381775},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.38429999351501465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3840000033378601},{"id":"https://openalex.org/C44359876","wikidata":"https://www.wikidata.org/wiki/Q5338467","display_name":"Edit distance","level":2,"score":0.3698999881744385},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.36660000681877136},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.3635999858379364},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3619000017642975},{"id":"https://openalex.org/C2779494224","wikidata":"https://www.wikidata.org/wiki/Q5645799","display_name":"Hamming space","level":5,"score":0.3422999978065491},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3393000066280365},{"id":"https://openalex.org/C2781166958","wikidata":"https://www.wikidata.org/wiki/Q1426863","display_name":"Suffix tree","level":3,"score":0.32100000977516174},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.29260000586509705},{"id":"https://openalex.org/C192028432","wikidata":"https://www.wikidata.org/wiki/Q845739","display_name":"Query language","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C24028149","wikidata":"https://www.wikidata.org/wiki/Q7094056","display_name":"Online aggregation","level":5,"score":0.28189998865127563},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2782999873161316},{"id":"https://openalex.org/C24755975","wikidata":"https://www.wikidata.org/wiki/Q4943354","display_name":"Boolean conjunctive query","level":5,"score":0.262800008058548},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.2551000118255615},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.01307","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01307","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.01307","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01307","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"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":{"A":[0,110],"classic":[1],"data":[2,129,186,250,294,313],"structure":[3,130,187,251,295],"problem":[4,41],"is":[5,86,113,119,131,170,212,227,266,281],"to":[6,103,133,258,267,274,300],"preprocess":[7],"a":[8,17,53,115,232,248],"string":[9],"T":[10,27],"of":[11,26,39,89,161,290,318],"length":[12],"$n$":[13],"so":[14],"that,":[15],"given":[16],"query":[18,36,73,147,164,189,216],"$q$,":[19],"we":[20,124,246,286,307],"can":[21,123],"quickly":[22],"find":[23],"all":[24,143],"substrings":[25],"with":[28,149,188,201],"Hamming":[29],"distance":[30],"at":[31],"most":[32],"$k$":[33],"from":[34],"the":[35,57,64,87,90,128,156,162,213,242,259,275,288,292,297,305],"string.":[37],"Variants":[38],"this":[40,137,211],"have":[42,146],"seen":[43,140],"significant":[44],"research":[45],"both":[46,291,312],"in":[47,50,256,284],"theory":[48],"and":[49,92,155,237,296],"practice.":[51],"For":[52],"wide":[54],"parameter":[55],"range,":[56],"best":[58,214],"worst-case":[59],"bounds":[60],"are":[61],"achieved":[62],"by":[63],"\"CGL":[65],"tree\"":[66],"(Cole,":[67],"Gottlieb,":[68],"Lewenstein":[69],"2004),":[70],"which":[71,315],"achieves":[72],"time":[74,148,165,190,217,236],"roughly":[75,171,191],"$\\tilde{O}(|q|":[76,172,192],"+":[77,80,173,176,179,193,196],"\\log^k":[78],"n":[79,178,195,198],"\\#":[81,180,199],"occ)$":[82],"where":[83],"$\\#":[84,225],"occ$":[85,226],"size":[88],"output,":[91],"space":[93,99,117,220,255],"${O}(n\\log^k":[94],"n)$.":[95],"The":[96,159],"CGL":[97,276,298],"Tree":[98],"was":[100],"recently":[101],"improved":[102,309],"$O(n":[104],"\\log^{k-1}":[105],"n)$":[106],"(Kociumaka,":[107],"Radoszewski":[108],"2026).":[109],"natural":[111],"question":[112,138],"whether":[114],"high":[116],"bound":[118],"necessary.":[120],"How":[121],"efficient":[122],"make":[125],"queries":[126],"when":[127],"constrained":[132],"$O(n)$":[134],"space?":[135],"While":[136],"has":[139],"extensive":[141],"research,":[142],"known":[144,215],"results":[145,230],"unfavorable":[150],"dependence":[151,203],"on":[152,204],"$n$,":[153],"$k$,":[154],"alphabet":[157],"$\u03a3$.":[158],"state":[160],"art":[163],"(Chan":[166],"et":[167],"al.":[168],"2011)":[169],"|\u03a3|^k":[174],"\\log^{k^2":[175],"k}":[177],"occ)$.":[181],"We":[182,239],"give":[183,231,241,247],"an":[184],"$O(n)$-space":[185],"\\log^{4k}":[194],"\\log^{2k}":[197],"occ)$,":[200],"no":[202],"$|\u03a3|$.":[205],"Even":[206],"if":[207,221],"$|\u03a3|":[208],"=":[209],"O(1)$,":[210],"for":[218,311],"linear":[219],"$k\\geq":[222],"3$":[223],"unless":[224],"large.":[228],"Our":[229,262],"smooth":[233],"tradeoff":[234],"between":[235],"space.":[238],"also":[240],"first":[243],"sublinear-space":[244],"results:":[245],"succinct":[249],"using":[252],"only":[253],"$o(n)$":[254],"addition":[257],"text":[260],"itself.":[261],"main":[263],"technical":[264],"idea":[265],"apply":[268],"function":[269],"inversion":[270],"(Fiat,":[271],"Naor":[272],"2000)":[273],"tree.":[277],"Combining":[278],"these":[279],"techniques":[280],"not":[282],"immediate;":[283],"fact,":[285],"revisit":[287],"exposition":[289],"Fiat-Naor":[293],"tree":[299],"obtain":[301,308],"our":[302],"bounds.":[303],"Along":[304],"way,":[306],"performance":[310],"structures,":[314],"may":[316],"be":[317],"independent":[319],"interest.":[320]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-04T00:00:00"}
