{"id":"https://openalex.org/W2077542803","doi":"https://doi.org/10.1145/1055531.1055537","title":"SFCGen: A framework for efficient generation of multi-dimensional space-filling curves by recursion","display_name":"SFCGen: A framework for efficient generation of multi-dimensional space-filling curves by recursion","publication_year":2005,"publication_date":"2005-03-01","ids":{"openalex":"https://openalex.org/W2077542803","doi":"https://doi.org/10.1145/1055531.1055537","mag":"2077542803"},"language":"en","primary_location":{"id":"doi:10.1145/1055531.1055537","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1055531.1055537","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"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 Mathematical Software","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/A5024096047","display_name":"Guohua Jin","orcid":"https://orcid.org/0000-0001-7853-2574"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Guohua Jin","raw_affiliation_strings":["Rice University, Houston, TX","Rice University (Houston, TX)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rice University, Houston, TX","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Rice University (Houston, TX)","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089709469","display_name":"John Mellor\u2010Crummey","orcid":"https://orcid.org/0000-0002-9026-5453"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Mellor-Crummey","raw_affiliation_strings":["Rice University, Houston, TX","Rice University (Houston, TX)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rice University, Houston, TX","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Rice University (Houston, TX)","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024096047"],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":null,"apc_paid":null,"fwci":3.7941,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.92994207,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"31","issue":"1","first_page":"120","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9979000091552734,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9979000091552734,"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.9860000014305115,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.984499990940094,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hilbert-curve","display_name":"Hilbert curve","score":0.6121853590011597},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5327762365341187},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5109509825706482},{"id":"https://openalex.org/keywords/search-engine-indexing","display_name":"Search engine indexing","score":0.5063518285751343},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5000452995300293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4672315716743469},{"id":"https://openalex.org/keywords/tree-traversal","display_name":"Tree traversal","score":0.4270886778831482},{"id":"https://openalex.org/keywords/hilbert-r-tree","display_name":"Hilbert R-tree","score":0.42435166239738464},{"id":"https://openalex.org/keywords/family-of-curves","display_name":"Family of curves","score":0.41384193301200867},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.2512856423854828},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.24700504541397095},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17508363723754883},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1171039342880249}],"concepts":[{"id":"https://openalex.org/C2781142347","wikidata":"https://www.wikidata.org/wiki/Q1366592","display_name":"Hilbert curve","level":2,"score":0.6121853590011597},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5327762365341187},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5109509825706482},{"id":"https://openalex.org/C75165309","wikidata":"https://www.wikidata.org/wiki/Q2258979","display_name":"Search engine indexing","level":2,"score":0.5063518285751343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5000452995300293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4672315716743469},{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.4270886778831482},{"id":"https://openalex.org/C76103427","wikidata":"https://www.wikidata.org/wiki/Q5761197","display_name":"Hilbert R-tree","level":5,"score":0.42435166239738464},{"id":"https://openalex.org/C53622353","wikidata":"https://www.wikidata.org/wiki/Q1518913","display_name":"Family of curves","level":2,"score":0.41384193301200867},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.2512856423854828},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.24700504541397095},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17508363723754883},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1171039342880249},{"id":"https://openalex.org/C60064506","wikidata":"https://www.wikidata.org/wiki/Q1262627","display_name":"Rigged Hilbert space","level":4,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1055531.1055537","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1055531.1055537","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"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 Mathematical Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W128912440","https://openalex.org/W1472640182","https://openalex.org/W1493714695","https://openalex.org/W1525420138","https://openalex.org/W1567484412","https://openalex.org/W1589213590","https://openalex.org/W1966612958","https://openalex.org/W1971379053","https://openalex.org/W1971434801","https://openalex.org/W1977041721","https://openalex.org/W1979605853","https://openalex.org/W1980180600","https://openalex.org/W1989187525","https://openalex.org/W1996833743","https://openalex.org/W2008045212","https://openalex.org/W2010733735","https://openalex.org/W2010769244","https://openalex.org/W2012647312","https://openalex.org/W2015190123","https://openalex.org/W2021426070","https://openalex.org/W2027787258","https://openalex.org/W2040879131","https://openalex.org/W2053197925","https://openalex.org/W2056402158","https://openalex.org/W2061291998","https://openalex.org/W2069896270","https://openalex.org/W2072605585","https://openalex.org/W2074056185","https://openalex.org/W2077520806","https://openalex.org/W2078900897","https://openalex.org/W2083298149","https://openalex.org/W2100668339","https://openalex.org/W2108730477","https://openalex.org/W2110418833","https://openalex.org/W2124222502","https://openalex.org/W2125955291","https://openalex.org/W2133927618","https://openalex.org/W2149122409","https://openalex.org/W2162169073","https://openalex.org/W2167594463","https://openalex.org/W2170236666","https://openalex.org/W2223384635","https://openalex.org/W2475750400","https://openalex.org/W2769954494","https://openalex.org/W4230059272","https://openalex.org/W4231010555","https://openalex.org/W4238485806","https://openalex.org/W4240774490","https://openalex.org/W4245825457","https://openalex.org/W4246962530","https://openalex.org/W6629731194","https://openalex.org/W6647694748","https://openalex.org/W6721025274"],"related_works":["https://openalex.org/W2521936059","https://openalex.org/W2393192391","https://openalex.org/W2065302945","https://openalex.org/W2390514042","https://openalex.org/W1602272796","https://openalex.org/W2336922657","https://openalex.org/W2146341593","https://openalex.org/W2527987597","https://openalex.org/W2050516347","https://openalex.org/W1571359635"],"abstract_inverted_index":{"Because":[0],"they":[1],"are":[2,47],"continuous":[3],"and":[4,86,136,152,155,173,176,220],"self-similar,":[5],"space-filling":[6,28,45,77,118,255],"curves":[7,29,46,59,78,154,175,256],"have":[8],"been":[9],"widely":[10],"used":[11,48,91],"in":[12,49,92,100],"mathematics":[13],"to":[14,73,89,113,124,139,207,222],"transform":[15,125],"multi-dimensional":[16,76],"problems":[17],"into":[18,130],"one-dimensional":[19],"forms.":[20],"For":[21],"scientific":[22],"applications,":[23],"reordering":[24,52],"computation":[25],"by":[26],"certain":[27],"can":[30,96,160],"significantly":[31],"improve":[32],"data":[33],"reuse":[34],"because":[35],"of":[36,40,57,127,180,225,244],"the":[37,58,69,80,134,141,178,186,211,248],"locality":[38],"properties":[39],"these":[41],"curves.":[42,193],"However,":[43],"when":[44],"programs":[50],"for":[51,170,267],"data,":[53],"traversal":[54],"or":[55],"indexing":[56,122],"must":[60],"be":[61,90,97,161],"efficient.":[62],"To":[63],"address":[64],"this":[65],"problem,":[66],"we":[67,146],"present":[68,167],"table-driven":[70],"framework":[71,83],"SFCGen":[72,204,237,260],"efficiently":[74],"generate":[75],"on":[79,190,197,216,253],"fly.":[81],"The":[82],"is":[84],"general":[85],"easy":[87],"enough":[88],"any":[93],"application":[94],"that":[95,203,259],"partitioned":[98],"recursively":[99],"multiple":[101],"dimensions.":[102],"We":[103,166],"describe":[104],"a":[105,109,117,120,128,156,223,242],"movement":[106],"specification":[107],"table,":[108],"universal":[110],"turtle":[111],"algorithm":[112,123,138,184,215],"enumerate":[114],"points":[115],"along":[116,133],"curve,":[119],"table-based":[121],"coordinates":[126],"point":[129],"its":[131],"position":[132],"curve":[135,159,182,218,235,265],"an":[137],"pregenerate":[140],"table":[142],"automatically.":[143],"As":[144],"examples,":[145],"show":[147,202,258],"how":[148],"high-dimensional":[149],"Hilbert,":[150,171],"Morton,":[151,172],"Peano":[153,174],"two-dimensional":[157],"Sierpi\u0144ski":[158],"generated":[162],"with":[163,185,264],"our":[164,181],"algorithms.":[165],"performance":[168],"results":[169,196,252],"compare":[177],"efficiency":[179],"generation":[183,219],"most":[187,212],"recent":[188,213],"work":[189],"generating":[191],"Hilbert":[192],"Our":[194,251],"experimental":[195],"three":[198,245],"modern":[199],"microprocessor-based":[200],"platforms":[201],"performs":[205,238],"up":[206,221],"63%":[208],"faster":[209,227,246],"than":[210,228,247],"recursive":[214],"2D":[217],"factor":[224,243],"132":[226],"two":[229],"previous":[230],"byte-oriented":[231,249],"non-recursive":[232],"implementations.":[233],"On":[234],"indexing,":[236],"as":[239,241],"much":[240],"implementation.":[250],"4D":[254],"also":[257],"scales":[261],"very":[262],"well":[263],"level":[266],"higher":[268],"dimensional":[269],"spaces.":[270]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":18}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
