{"id":"https://openalex.org/W2129335013","doi":"https://doi.org/10.1142/s0218195992000044","title":"ENUMERATING INTERDISTANCES IN SPACE","display_name":"ENUMERATING INTERDISTANCES IN SPACE","publication_year":1992,"publication_date":"1992-03-01","ids":{"openalex":"https://openalex.org/W2129335013","doi":"https://doi.org/10.1142/s0218195992000044","mag":"2129335013"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195992000044","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195992000044","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","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/A5015854490","display_name":"Jeffrey S. Salowe","orcid":null},"institutions":[{"id":"https://openalex.org/I51556381","display_name":"University of Virginia","ror":"https://ror.org/0153tk833","country_code":"US","type":"education","lineage":["https://openalex.org/I51556381"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JEFFREY S. SALOWE","raw_affiliation_strings":["Department of Computer Science, University of Virginia, Thornton Hall, Charlottesville, Virginia 22903, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Virginia, Thornton Hall, Charlottesville, Virginia 22903, USA","institution_ids":["https://openalex.org/I51556381"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015854490"],"corresponding_institution_ids":["https://openalex.org/I51556381"],"apc_list":null,"apc_paid":null,"fwci":1.9942,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.85890909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"02","issue":"01","first_page":"49","last_page":"59"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9818999767303467,"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":0.9818999767303467,"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/T11502","display_name":"Facility Location and Emergency Management","score":0.963699996471405,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9606999754905701,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8480854034423828},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.8323231935501099},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8160160779953003},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6184987425804138},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.604265034198761},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5467182993888855},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5343984961509705},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.4660220146179199},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44700315594673157},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.4461631178855896},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4399043023586273},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4307190179824829},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.41984283924102783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07164549827575684}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8480854034423828},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8323231935501099},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8160160779953003},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6184987425804138},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.604265034198761},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5467182993888855},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5343984961509705},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.4660220146179199},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44700315594673157},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.4461631178855896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4399043023586273},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4307190179824829},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.41984283924102783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07164549827575684},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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:10.1142/s0218195992000044","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195992000044","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W2143566611","https://openalex.org/W2013740965","https://openalex.org/W588267724","https://openalex.org/W4297743441","https://openalex.org/W2952598754","https://openalex.org/W2026779193"],"abstract_inverted_index":{"In":[0],"this":[1,164],"paper,":[2],"we":[3],"study":[4],"the":[5,9,21,33,53,96,108,128,148],"enumerative":[6],"versions":[7],"of":[8,41,56,59,98,115,133],"interdistance":[10,26,62,109,140,149],"in":[11,18,90],"terdis":[12],"stance":[13],"ranking":[14],"and":[15,25,46,52,120,127],"selection":[16],"problems":[17],"space,":[19],"namely,":[20],"fixed-radius":[22,34,79],"near":[23,35,80],"neighbors":[24,36,81],"enumeration":[27,110],"problems,":[28],"respectively.":[29],"The":[30,100,105],"input":[31,106],"to":[32,85,107,138,147],"problem":[37,111],"is":[38,95,103,112,130],"a":[39,47,78,113,131],"set":[40,114,132],"n":[42,116],"points":[43,60,117],"S\u2286\u211c":[44],"d":[45,119],"nonnegative":[48],"real":[49],"number":[50],"\u03b4,":[51],"output":[54,129],"consists":[55],"all":[57],"pairs":[58],"within":[61],"\u03b4.":[63,99],"We":[64,153],"give":[65],"an":[66,70,86,121,139,155],"algorithm":[67,162,167],"which,":[68],"after":[69],"O(n":[71,156],"log":[72,157],"n)":[73],"time":[74],"preprocessing":[75],"step,":[76],"answers":[77],"query":[82],"with":[83,150],"respect":[84],"L":[87,172],"p":[88,173],"metric":[89],"O(n+\u03c1(\u03b4))":[91],"time,":[92,159],"where":[93],"\u03c1(\u03b4)":[94],"rank":[97,151],"space":[101,161],"needed":[102],"O(n).":[104],"S\u20c4\u211c":[118],"integer":[122],"k,":[123],"[Formula:":[124],"see":[125],"text],":[126],"point":[134],"pairs,":[135],"each":[136],"corresponding":[137],"having":[141],"length":[142],"less":[143],"than":[144],"or":[145],"equal":[146],"k.":[152],"offer":[154],"n+k)":[158],"O(n+k)":[160],"for":[163,170],"problem.":[165],"This":[166],"also":[168],"works":[169],"any":[171],"metric.":[174]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
