{"id":"https://openalex.org/W4303195670","doi":"https://doi.org/10.1142/s0218195922500054","title":"Efficient Predicate Evaluation Using Randomized Degeneracy Detection","display_name":"Efficient Predicate Evaluation Using Randomized Degeneracy Detection","publication_year":2022,"publication_date":"2022-03-01","ids":{"openalex":"https://openalex.org/W4303195670","doi":"https://doi.org/10.1142/s0218195922500054"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195922500054","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195922500054","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/A5039907465","display_name":"Victor Milenkovic","orcid":"https://orcid.org/0000-0001-8524-9742"},"institutions":[{"id":"https://openalex.org/I145608581","display_name":"University of Miami","ror":"https://ror.org/02dgjyy92","country_code":"US","type":"education","lineage":["https://openalex.org/I145608581"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Victor Milenkovic","raw_affiliation_strings":["Department of Computer Science, University of Miami, Coral Gables, Floridy 33124-4245, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Miami, Coral Gables, Floridy 33124-4245, USA","institution_ids":["https://openalex.org/I145608581"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035745117","display_name":"Elisha Sacks","orcid":"https://orcid.org/0009-0002-6955-2754"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elisha Sacks","raw_affiliation_strings":["Computer Science Department, Purdue University, West Lafayette, Indiana 47907-2066, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, Purdue University, West Lafayette, Indiana 47907-2066, USA","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1437,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49311703,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"32","issue":"01n02","first_page":"39","last_page":"54"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9972000122070312,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9972000122070312,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9945999979972839,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9908000230789185,"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/degeneracy","display_name":"Degeneracy (biology)","score":0.7516257166862488},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.6729370951652527},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6582585573196411},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6212280988693237},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6101254820823669},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5176025629043579},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5066045522689819},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.42284345626831055},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35934287309646606},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3235197365283966},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18180489540100098}],"concepts":[{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.7516257166862488},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6729370951652527},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6582585573196411},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6212280988693237},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6101254820823669},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5176025629043579},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5066045522689819},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.42284345626831055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35934287309646606},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3235197365283966},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18180489540100098},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195922500054","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195922500054","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":[{"id":"https://openalex.org/G4896173053","display_name":"AF: Small: Collaborative Research: Making Computational Geometry Polynomial in Derivation Length and in Dimension","funder_award_id":"1524455","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5476803808","display_name":"AF:Small:Collaborative Research:Making Computational Geometry Polynomial in Derivation Length and in Dimension","funder_award_id":"1526335","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1501243125","https://openalex.org/W1580809199","https://openalex.org/W1606309972","https://openalex.org/W1969213662","https://openalex.org/W1980856175","https://openalex.org/W1986405515","https://openalex.org/W1990564835","https://openalex.org/W2009209832","https://openalex.org/W2057280919","https://openalex.org/W2060760900","https://openalex.org/W2061179469","https://openalex.org/W2071577157","https://openalex.org/W2080666584","https://openalex.org/W2116476963","https://openalex.org/W2119352997","https://openalex.org/W2134277629","https://openalex.org/W2155762515","https://openalex.org/W2245029098","https://openalex.org/W2621386816","https://openalex.org/W2962736818","https://openalex.org/W2982239602","https://openalex.org/W4210777595"],"related_works":["https://openalex.org/W2125277162","https://openalex.org/W168460013","https://openalex.org/W1552514155","https://openalex.org/W4287687395","https://openalex.org/W2215112080","https://openalex.org/W3037733829","https://openalex.org/W4300428659","https://openalex.org/W2955288804","https://openalex.org/W2124225859","https://openalex.org/W2026856841"],"abstract_inverted_index":{"Computational":[0],"geometry":[1],"algorithms":[2,40,143],"branch":[3],"on":[4,15,21,23,54,68],"the":[5,82,94,157,159,162,168],"signs":[6],"of":[7,96,170],"predicates.":[8],"Prior":[9],"predicate":[10,186],"evaluation":[11,187],"techniques":[12],"are":[13,125,144],"slow":[14],"degenerate":[16,52,66,121],"(zero":[17],"sign)":[18],"predicates,":[19,74],"especially":[20],"predicates":[22,30,53,67,123],"algebraic":[24,69,97,122],"numbers.":[25,56],"Degeneracy":[26],"is":[27,87,91,101,188],"common":[28,34],"for":[29,41],"whose":[31],"arguments":[32],"have":[33],"antecedents.":[35],"We":[36,174],"present":[37],"three":[38],"randomized":[39],"degeneracy":[42,163,179],"detection.":[43],"The":[44,57,113,139],"first":[45,83,140],"algorithm":[46,59,86,115],"uses":[47,60,109,116],"modular":[48],"arithmetic":[49],"to":[50,63,71,119,128,134],"detect":[51,135],"rational":[55,73],"second":[58,132],"quotient":[61],"rings":[62],"reduce":[64],"detecting":[65],"numbers":[70],"multiple":[72],"which":[75],"can":[76],"be":[77],"evaluated":[78],"deterministically":[79],"or":[80],"using":[81],"algorithm.":[84],"This":[85],"impractical":[88],"because":[89],"it":[90,100],"exponential":[92],"in":[93],"number":[95],"numbers,":[98],"yet":[99],"still":[102],"much":[103],"faster":[104],"than":[105],"prior":[106],"work":[107],"that":[108,124,137,185],"root":[110],"separation":[111],"bounds.":[112],"third":[114,142],"a":[117,131],"perturbation":[118,133],"eliminate":[120],"not":[126],"identical":[127],"zero":[129],"and":[130,141,190],"those":[136],"are.":[138],"incorporated":[145],"into":[146],"an":[147],"exact":[148],"geometric":[149],"computation":[150],"library.":[151],"By":[152],"sampling":[153],"values":[154],"generated":[155],"by":[156],"algorithms,":[158],"library":[160],"estimates":[161],"detection":[164,180],"failure":[165],"probability":[166],"over":[167],"lifetime":[169],"every":[171],"calling":[172],"program.":[173],"call":[175],"this":[176],"approach":[177],"statistical":[178],"(SDD).":[181],"Extensive":[182],"testing":[183],"shows":[184],"reliable":[189],"fast.":[191]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
