{"id":"https://openalex.org/W7225593164","doi":"https://doi.org/10.5281/zenodo.24056147","title":"KNIGHT: Exact Local Certificates and Sharp Cost Separations in Variable-Elimination Ordering","display_name":"KNIGHT: Exact Local Certificates and Sharp Cost Separations in Variable-Elimination Ordering","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225593164","doi":"https://doi.org/10.5281/zenodo.24056147"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24056147","doi":"https://doi.org/10.5281/zenodo.24056147","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24056147","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24056147","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078115449","display_name":"Md. Amir Khusru Akhtar","orcid":"https://orcid.org/0000-0002-3432-4199","observed_orcids":["https://orcid.org/0000-0002-3432-4199"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Akhtar, Mohammad Amir Khusru","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3432-4199","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5078115449"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.4805000126361847,"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"}},"topics":[{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.4805000126361847,"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":0.37229999899864197,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0658000037074089,"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/variable-elimination","display_name":"variable elimination","score":0.5960000157356262},{"id":"https://openalex.org/keywords/cnf","display_name":"CNF","score":0.7129999995231628},{"id":"https://openalex.org/keywords/resolution","display_name":"resolution","score":0.47099998593330383},{"id":"https://openalex.org/keywords/subsumption","display_name":"subsumption","score":0.9789999723434448},{"id":"https://openalex.org/keywords/elimination-orderings","display_name":"elimination orderings","score":0.6620000004768372},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"dynamic programming","score":0.7110000252723694}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6662999987602234},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5511999726295471},{"id":"https://openalex.org/C96865113","wikidata":"https://www.wikidata.org/wiki/Q2946816","display_name":"Certificate","level":2,"score":0.5},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.4860000014305115},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.42980000376701355},{"id":"https://openalex.org/C75165309","wikidata":"https://www.wikidata.org/wiki/Q2258979","display_name":"Search engine indexing","level":2,"score":0.4194999933242798},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39259999990463257},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3862000107765198},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36970001459121704},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3009999990463257},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C169272836","wikidata":"https://www.wikidata.org/wiki/Q5668307","display_name":"Variable elimination","level":3,"score":0.29499998688697815},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27950000762939453},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26759999990463257},{"id":"https://openalex.org/C168956720","wikidata":"https://www.wikidata.org/wiki/Q3123181","display_name":"Column generation","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26420000195503235},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.2583000063896179}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24056147","doi":"https://doi.org/10.5281/zenodo.24056147","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24056147","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24056148","doi":"https://doi.org/10.5281/zenodo.24056148","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24056148","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24056147","doi":"https://doi.org/10.5281/zenodo.24056147","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24056147","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7097197756","https://openalex.org/W4391174184","https://openalex.org/W2026461558","https://openalex.org/W7213357210","https://openalex.org/W1564470442","https://openalex.org/W1776544432","https://openalex.org/W285322218","https://openalex.org/W2573054537","https://openalex.org/W7100585496","https://openalex.org/W2522559094"],"abstract_inverted_index":{"The":[0,181],"size":[1],"of":[2,116],"a":[3,31,144,194],"CNF":[4,67,140],"formula":[5],"after":[6],"variable":[7],"elimination":[8,26,134],"depends":[9],"on":[10,86,107],"the":[11,53,70,77,112,151,161,167],"interaction":[12],"between":[13,24],"resolution,":[14],"tautology":[15],"removal,":[16],"and":[17,28,44,58,76],"subsumption.":[18],"We":[19,129],"investigate":[20],"exact":[21,49,196,208],"one-step":[22],"comparisons":[23,75,206],"candidate":[25],"pivots":[27],"develop":[29],"KNIGHT,":[30],"certificate":[32,96],"framework":[33],"that":[34,80],"establishes":[35],"strict":[36],"normalized":[37],"clause-count":[38,205],"dominance":[39],"from":[40,98,143],"surviving-background":[41],"lower":[42],"bounds":[43],"minimal-resolvent":[45],"upper":[46],"bounds.":[47],"An":[48],"slack":[50],"identity":[51],"characterizes":[52],"bounds,":[54],"while":[55],"incremental":[56,82],"inspection":[57],"tautology-aware":[59],"indexing":[60,93],"provide":[61],"complementary":[62],"certification":[63],"procedures.":[64],"Two":[65],"parameterized":[66],"families":[68],"identify":[69],"information":[71],"captured":[72],"by":[73],"local":[74,204],"quadratic":[78],"work":[79],"an":[81,137],"procedure":[83],"may":[84],"incur":[85],"tautological":[87],"resolvent":[88],"pairs.":[89],"In":[90],"constructed":[91,142],"instances,":[92],"reduces":[94],"median":[95],"time":[97],"9.15":[99],"to":[100,121,164],"0.88":[101],"ms,":[102],"with":[103,166,207],"higher":[104],"traced":[105],"allocation;":[106],"1,000":[108],"seeded":[109],"random":[110],"comparisons,":[111],"methods":[113],"certify":[114],"10":[115],"406":[117],"favorable":[118],"cases,":[119],"increasing":[120],"12":[122],"when":[123],"one":[124],"successor":[125],"is":[126,154,171,185],"evaluated":[127],"exactly.":[128],"further":[130],"establish":[131],"sharp":[132],"cumulative":[133],"costs":[135],"for":[136,177],"infinite":[138],"connected":[139,149],"family":[141],"seven-clause":[145],"gadget.":[146],"For":[147],"k":[148,178],"copies,":[150],"unrestricted":[152],"optimum":[153,162],"(11k\u00b2":[155,172],"+":[156,173],"19k":[157],"\u2212":[158,175,188],"10)/2,":[159],"whereas":[160],"constrained":[163],"begin":[165],"locally":[168],"smallest":[169],"pivot":[170],"25k":[174],"16)/2":[176],"\u2265":[179],"2.":[180],"resulting":[182],"additive":[183],"separation":[184],"exactly":[186],"3k":[187],"3.":[189],"A":[190],"shared-positive-variable":[191],"decomposition":[192],"yields":[193],"symmetry-reduced":[195],"dynamic":[197],"program.":[198],"Together,":[199],"these":[200],"results":[201],"connect":[202],"verifiable":[203],"global":[209],"elimination-order":[210],"analysis.":[211]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}
