{"id":"https://openalex.org/W2038987765","doi":"https://doi.org/10.1137/0222023","title":"Average Time Analysis of Clause Order Backtracking","display_name":"Average Time Analysis of Clause Order Backtracking","publication_year":1993,"publication_date":"1993-04-01","ids":{"openalex":"https://openalex.org/W2038987765","doi":"https://doi.org/10.1137/0222023","mag":"2038987765"},"language":"en","primary_location":{"id":"doi:10.1137/0222023","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0222023","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/A5024034979","display_name":"Khaled M. Bugrara","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Khaled M. Bugrara","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030220389","display_name":"Paul W. Purdom","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul Walton Purdom, Jr.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024034979"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0425,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76073758,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"2","first_page":"303","last_page":"317"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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":0.9994999766349792,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9987000226974487,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.996999979019165,"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/backtracking","display_name":"Backtracking","score":0.9591462016105652},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7090372443199158},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.6243038177490234},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.605663537979126},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5816393494606018},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5510103702545166},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.49185776710510254},{"id":"https://openalex.org/keywords/literal","display_name":"Literal (mathematical logic)","score":0.48374438285827637},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4761359989643097},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.46681639552116394},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.44573190808296204},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2360251247882843},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.058676689863204956}],"concepts":[{"id":"https://openalex.org/C156884757","wikidata":"https://www.wikidata.org/wiki/Q798554","display_name":"Backtracking","level":2,"score":0.9591462016105652},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7090372443199158},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.6243038177490234},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.605663537979126},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5816393494606018},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5510103702545166},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.49185776710510254},{"id":"https://openalex.org/C2780882242","wikidata":"https://www.wikidata.org/wiki/Q14235582","display_name":"Literal (mathematical logic)","level":2,"score":0.48374438285827637},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4761359989643097},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.46681639552116394},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.44573190808296204},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2360251247882843},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.058676689863204956},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0222023","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0222023","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"},{"id":"pmh:hdl:10068/178851","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/178851","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1550402024","https://openalex.org/W1995067748","https://openalex.org/W2010848428","https://openalex.org/W2016042296","https://openalex.org/W2021126666","https://openalex.org/W2037712946","https://openalex.org/W2050917944","https://openalex.org/W2055978814","https://openalex.org/W2076342862"],"related_works":["https://openalex.org/W1540360785","https://openalex.org/W3123395501","https://openalex.org/W4287372456","https://openalex.org/W2028837121","https://openalex.org/W2128025986","https://openalex.org/W1488898519","https://openalex.org/W2050917944","https://openalex.org/W2076477022","https://openalex.org/W1995067748","https://openalex.org/W2089872375"],"abstract_inverted_index":{"Backtracking":[0],"aigorithms":[1],"solve":[2],"problems":[3],"by":[4,56],"selecting":[5],"a":[6,29,76,80,84,169],"variable":[7],"and":[8,21,75,151],"assigning":[9],"each":[10],"possible":[11],"value":[12],"to":[13,103,134],"the":[14,38,52,67,129,173],"variable.":[15],"The":[16,86],"resulting":[17],"subproblems":[18],"are":[19,49],"simplified":[20],"solved":[22],"recursively.":[23],"Simple":[24],"backtracking":[25,34,59,92,111,120],"selects":[26,35],"variables":[27,36],"in":[28,83,172],"fixed":[30],"order.":[31],"Clause":[32],"order":[33,58,91,119],"from":[37],"first":[39],"nontrivial":[40],"clause":[41,57,90,118],"that":[42,97],"has":[43],"not":[44],"yet":[45],"been":[46],"satisfied.":[47],"Formulas":[48],"given":[50],"for":[51,89,98],"average":[53,87,114,122],"time":[54,88,105,123],"used":[55],"when":[60,178],"solving":[61],"random":[62],"CNF":[63],"satisfiability":[64],"problems,":[65],"where":[66,109,117],"problem":[68],"sets":[69],"have":[70],"v":[71,132,144],"variables,":[72],"t":[73,156,179],"clauses,":[74],"probability":[77],"p":[78],"of":[79,131,175],"literal":[81],"being":[82],"clause.":[85],"is":[93],"always":[94],"less":[95,124],"than":[96,125,182],"simple":[99,110],"backtracking.":[100],"It":[101],"leads":[102],"polynomial":[104],"under":[106],"many":[107],"conditions":[108],"uses":[112,121],"exponential":[113],"time.":[115],"Cases":[116],"$v^n":[126],"$":[127,150],"(in":[128],"limit":[130],"going":[133],"infinity)":[135],"include":[136],"$p":[137,152],"<":[138],"{1":[139],"/":[140,148,160,162],"{(2v)}}e^{{{[(n":[141],"-":[142,145],"1)\\ln":[143],"\\ln":[146],"t]}":[147],"t}}":[149],">":[153],"\\sqrt":[154],"{[\\ln":[155],"+":[157],"{{{{(\\ln":[158],"v)}":[159],"2}]}":[161],"v}}":[163],"$.":[164],"(The":[165],"second":[166],"result":[167],"needs":[168],"slight":[170],"increase":[171],"coefficient":[174],"$\\ln":[176],"t$":[177],"increases":[180],"faster":[181],"$v^{\\ln":[183],"v}":[184],"$.)":[185]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
