{"id":"https://openalex.org/W2039404537","doi":"https://doi.org/10.1137/s0097539795298321","title":"Two-Dimensional Periodicity in Rectangular Arrays","display_name":"Two-Dimensional Periodicity in Rectangular Arrays","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2039404537","doi":"https://doi.org/10.1137/s0097539795298321","mag":"2039404537"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539795298321","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539795298321","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048790288","display_name":"Amihood Amir","orcid":"https://orcid.org/0000-0002-3939-337X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amihood Amir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065328235","display_name":"Gary Benson","orcid":"https://orcid.org/0000-0003-2374-5462"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gary Benson","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":3.7834,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.93928068,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"27","issue":"1","first_page":"90","last_page":"106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"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":0.9998999834060669,"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/T12326","display_name":"Network Packet Processing and Optimization","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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":0.9975000023841858,"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/rectangle","display_name":"Rectangle","score":0.7487667798995972},{"id":"https://openalex.org/keywords/string-searching-algorithm","display_name":"String searching algorithm","score":0.7471034526824951},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6166371703147888},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5474449396133423},{"id":"https://openalex.org/keywords/pattern-matching","display_name":"Pattern matching","score":0.541961669921875},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5322781801223755},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4839220643043518},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.46524226665496826},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4619244933128357},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.45058673620224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42250651121139526},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38358086347579956},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22410422563552856},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11174994707107544}],"concepts":[{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.7487667798995972},{"id":"https://openalex.org/C7757238","wikidata":"https://www.wikidata.org/wiki/Q374040","display_name":"String searching algorithm","level":3,"score":0.7471034526824951},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6166371703147888},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5474449396133423},{"id":"https://openalex.org/C68859911","wikidata":"https://www.wikidata.org/wiki/Q1503724","display_name":"Pattern matching","level":2,"score":0.541961669921875},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5322781801223755},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4839220643043518},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.46524226665496826},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4619244933128357},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.45058673620224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42250651121139526},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38358086347579956},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22410422563552856},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11174994707107544},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0097539795298321","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539795298321","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.47.200","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.200","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.biu.ac.il/~amir/Postscripts/period.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.2643","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.2643","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://tandem.bu.edu/papers/2D.periodicity.in.rect.arrays.siam.jc.1998.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1607302839","https://openalex.org/W1973456884","https://openalex.org/W1975363716","https://openalex.org/W1983343295","https://openalex.org/W1984398316","https://openalex.org/W1984548556","https://openalex.org/W1985108724","https://openalex.org/W1991454799","https://openalex.org/W2002730083","https://openalex.org/W2003200876","https://openalex.org/W2011999472","https://openalex.org/W2022657287","https://openalex.org/W2024557852","https://openalex.org/W2032995245","https://openalex.org/W2046946959","https://openalex.org/W2073908457","https://openalex.org/W2084403744","https://openalex.org/W2099964107","https://openalex.org/W2111297109","https://openalex.org/W2134826720","https://openalex.org/W2143410463","https://openalex.org/W2143462372","https://openalex.org/W2143991273","https://openalex.org/W2153048767","https://openalex.org/W2159166270","https://openalex.org/W2160748429","https://openalex.org/W2533248932","https://openalex.org/W4212840250"],"related_works":["https://openalex.org/W3145288231","https://openalex.org/W2371263218","https://openalex.org/W2092552144","https://openalex.org/W2354196777","https://openalex.org/W2965473297","https://openalex.org/W2108265183","https://openalex.org/W2257399947","https://openalex.org/W2248278495","https://openalex.org/W2386746909","https://openalex.org/W2387316851"],"abstract_inverted_index":{"String":[0],"matching":[1,13,56],"is":[2,44,61,67,97,111,207],"rich":[3],"with":[4],"a":[5,16,25,99,105,120,123,179],"variety":[6],"of":[7,20,94,119,126,141,157],"algorithmic":[8,27],"tools.":[9],"In":[10,80,174],"contrast,":[11],"multidimensional":[12],"has":[14,50],"had":[15],"rather":[17],"sparse":[18],"set":[19],"techniques.":[21],"This":[22],"paper":[23],"presents":[24],"new":[26],"technique":[28],"for":[29],"two-dimensional":[30,87],"matching:":[31],"periodicity":[32,88,96],"analysis.":[33],"Its":[34],"strength":[35],"appears":[36],"to":[37,53],"lie":[38],"in":[39,48,68,77,89,104,113,188,196,210,220],"the":[40,129,155,158,183,204],"fact":[41],"that":[42,98,166,182],"it":[43,66],"inherently":[45],"two-dimensional.":[46],"Periodicity":[47],"strings":[49,69],"been":[51],"used":[52,76],"solve":[54],"string":[55,95,101],"problems.":[57],"Multidimensional":[58],"periodicity,":[59],"however,":[60],"not":[62,72,186],"as":[63,65],"simple":[64],"and":[70,85,149,163,209],"was":[71],"formally":[73],"studied":[74],"or":[75],"pattern":[78,125],"matching.":[79],"this":[81,135],"paper,":[82],"we":[83,137],"define":[84,138],"analyze":[86],"rectangular":[90],"arrays.":[91],"One":[92],"definition":[93],"periodic":[100,142],"can":[102],"self-overlap":[103,117,187],"particular":[106],"way.":[107],"An":[108],"analogous":[109],"concept":[110],"true":[112],"two":[114],"dimensions.":[115],"The":[116,192,216],"vectors":[118],"rectangle":[121,130],"generate":[122],"regular":[124],"locations":[127,169],"where":[128,170],"may":[131],"originate.":[132],"Based":[133],"on":[134],"regularity,":[136],"four":[139],"categories":[140],"arrays---":[143],"nonperiodic,":[144],"lattice":[145],"periodic,":[146,148],"line":[147],"radiant":[150],"periodic---and":[151],"prove":[152],"theorems":[153],"about":[154],"properties":[156],"classes.":[159],"We":[160],"give":[161],"serial":[162,193],"parallel":[164,217],"algorithms":[165,177],"find":[167,178],"all":[168],"an":[171],"overlap":[172],"originates.":[173],"addition,":[175],"our":[176],"witness":[180],"proving":[181],"array":[184],"does":[185],"any":[189],"other":[190],"location.":[191],"algorithm":[194,218],"runs":[195,219],"time":[197,221],"O(m":[198,211,225],"2":[199,212,226],")":[200,227],"(linear":[201],"time)":[202],"when":[203],"alphabet":[205],"size":[206],"finite,":[208],"log":[213],"m)":[214,223],"otherwise.":[215],"O(log":[222],"using":[224],"CRCW":[228],"processors.":[229]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
