{"id":"https://openalex.org/W2019609597","doi":"https://doi.org/10.1137/s0097539791256325","title":"Improved Algorithms For Linear Inequalities with Two Variables Per Inequality","display_name":"Improved Algorithms For Linear Inequalities with Two Variables Per Inequality","publication_year":1994,"publication_date":"1994-12-01","ids":{"openalex":"https://openalex.org/W2019609597","doi":"https://doi.org/10.1137/s0097539791256325","mag":"2019609597"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539791256325","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539791256325","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/A5026385549","display_name":"Edith Cohen","orcid":"https://orcid.org/0000-0002-3926-8237"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Edith Cohen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019904083","display_name":"Nimrod Megiddo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nimrod Megiddo","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026385549"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4615,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.80325027,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"23","issue":"6","first_page":"1313","last_page":"1347"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9983999729156494,"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/T12288","display_name":"Optimization and Search Problems","score":0.9983999729156494,"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":0.6976654529571533},{"id":"https://openalex.org/keywords/tilde","display_name":"Tilde","score":0.661955714225769},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.588589608669281},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.5193842053413391},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4802165925502777},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3472471833229065}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6976654529571533},{"id":"https://openalex.org/C36686422","wikidata":"https://www.wikidata.org/wiki/Q11167","display_name":"Tilde","level":2,"score":0.661955714225769},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.588589608669281},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.5193842053413391},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4802165925502777},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3472471833229065}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0097539791256325","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539791256325","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1486906909","https://openalex.org/W1584086289","https://openalex.org/W2000472767","https://openalex.org/W2002636386","https://openalex.org/W2005347459","https://openalex.org/W2018344976","https://openalex.org/W2019609597","https://openalex.org/W2035144082","https://openalex.org/W2038183039","https://openalex.org/W2039394406","https://openalex.org/W2073873127","https://openalex.org/W2085048392","https://openalex.org/W2090286414","https://openalex.org/W2100922675","https://openalex.org/W2103985627","https://openalex.org/W2752885492","https://openalex.org/W4230818032"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2348766922","https://openalex.org/W3128905785","https://openalex.org/W1978225469","https://openalex.org/W2799759016","https://openalex.org/W3104631496","https://openalex.org/W2093911591","https://openalex.org/W2049729887","https://openalex.org/W2076027639","https://openalex.org/W2000144448"],"abstract_inverted_index":{"The":[0,76,83],"authors":[1],"show":[2],"that":[3],"a":[4],"system":[5],"of":[6,50,94],"m":[7],"linear":[8],"inequalities":[9],"with":[10],"n":[11],"variables,":[12,20],"where":[13,58],"each":[14],"inequality":[15],"involves":[16],"at":[17],"most":[18],"two":[19],"can":[21],"be":[22],"solved":[23],"in":[24,39,54],"$\\tilde":[25,31,40,55,63,71],"O(mn^2":[26],")$":[27],"time":[28,45],"(we":[29],"denote":[30],"O(f)":[32],"=":[33],"O(f{\\operatorname{polylog}}":[34],"n{\\operatorname{polylog}}":[35],"m))$":[36],"deterministically,":[37],"and":[38,66],"O(n^3":[41],"+":[42,73],"mn)$":[43],"expected":[44],"using":[46],"randomization.":[47],"Parallel":[48],"implementations":[49],"these":[51],"algorithms":[52],"run":[53],"O(n)$":[56],"time,":[57],"the":[59,67,92,95],"deterministic":[60],"algorithm":[61,69,85],"uses":[62,70],"O(mn)$":[64],"processors":[65],"randomized":[68,84],"O(n^2":[72],"m)$":[74],"processors.":[75],"bounds":[77],"significantly":[78],"improve":[79],"over":[80],"previous":[81],"algorithms.":[82],"is":[86],"based":[87],"on":[88],"novel":[89],"insights":[90],"into":[91],"structure":[93],"problem.":[96]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
