{"id":"https://openalex.org/W2081575358","doi":"https://doi.org/10.1080/00207169908804812","title":"Partitioning ideal sets","display_name":"Partitioning ideal sets","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2081575358","doi":"https://doi.org/10.1080/00207169908804812","mag":"2081575358"},"language":"en","primary_location":{"id":"doi:10.1080/00207169908804812","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804812","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5056385597","display_name":"Robert R. Goldberg","orcid":null},"institutions":[{"id":"https://openalex.org/I111455621","display_name":"Queens College, CUNY","ror":"https://ror.org/03v8adn41","country_code":"US","type":"education","lineage":["https://openalex.org/I111455621"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert R. Goldberg","raw_affiliation_strings":["Queens College , Cuny"],"affiliations":[{"raw_affiliation_string":"Queens College , Cuny","institution_ids":["https://openalex.org/I111455621"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026965380","display_name":"Jacob Shapiro","orcid":null},"institutions":[{"id":"https://openalex.org/I141810926","display_name":"Baruch College","ror":"https://ror.org/023qavy03","country_code":"US","type":"education","lineage":["https://openalex.org/I141810926"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jacob Shapiro","raw_affiliation_strings":["Dept. of Statistics and Computer Information Systems , Baruch College , New York, NY, 10010"],"affiliations":[{"raw_affiliation_string":"Dept. of Statistics and Computer Information Systems , Baruch College , New York, NY, 10010","institution_ids":["https://openalex.org/I141810926"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056385597"],"corresponding_institution_ids":["https://openalex.org/I111455621"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20247796,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"3","first_page":"337","last_page":"349"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9983999729156494,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8184486031532288},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6416927576065063},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.637686550617218},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6366910934448242},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5457366108894348},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5081362724304199},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49864673614501953},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.44694963097572327},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12217625975608826}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8184486031532288},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6416927576065063},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.637686550617218},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6366910934448242},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5457366108894348},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5081362724304199},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49864673614501953},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.44694963097572327},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12217625975608826},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169908804812","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804812","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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":9,"referenced_works":["https://openalex.org/W1537316992","https://openalex.org/W1608311021","https://openalex.org/W1990313671","https://openalex.org/W1999370138","https://openalex.org/W2001016215","https://openalex.org/W2018838693","https://openalex.org/W2104680817","https://openalex.org/W2886788475","https://openalex.org/W4301358660"],"related_works":["https://openalex.org/W2383873009","https://openalex.org/W2590472383","https://openalex.org/W2393580911","https://openalex.org/W2212184297","https://openalex.org/W3207130397","https://openalex.org/W3156456913","https://openalex.org/W3129784286","https://openalex.org/W2390945180","https://openalex.org/W2394052932","https://openalex.org/W2737552886"],"abstract_inverted_index":{"This":[0,59],"paper":[1,75],"analyzes":[2],"a":[3,15,49,80,91],"class":[4,110],"of":[5,13,18,96,111],"approximation":[6],"algorithms":[7],"for":[8,36,99,107],"the":[9,37,42,56,100,108],"NP-complete":[10],"problem":[11,46],"[4]":[12],"partitioning":[14],"given":[16],"set":[17],"positive":[19],"real":[20],"numbers":[21],"into":[22],"k":[23],"subsets.":[24],"Chandra":[25],"and":[26,47,66],"Wong":[27],"[2]":[28],"analyzed":[29],"one":[30],"such":[31,105],"algorithm":[32],"(Graham's":[33],"LPT":[34],"rule)":[35],"L":[38,101],"2":[39,102],"metric":[40],"on":[41,104],"related":[43],"classic":[44],"scheduling":[45],"proved":[48],"25/24":[50],"worst":[51],"case":[52],"upper":[53,94],"bound":[54,95],"in":[55,73],"general":[57],"case.":[58],"result":[60],"was":[61],"slightly":[62],"improved":[63],"by":[64],"Leung":[65],"Wei":[67],"[9].":[68],"The":[69],"input":[70],"sets":[71,77,106],"considered":[72],"this":[74],"are":[76],"which":[78],"have":[79],"k-partition":[81],"with":[82],"equal":[83],"sum":[84],"subsets":[85],"(termed":[86],"ideal":[87],"sets);":[88],"we":[89],"prove":[90],"new":[92],"tight":[93],"37/":[97],"36":[98],"norm":[103],"entire":[109],"algorithms.":[112]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}