{"id":"https://openalex.org/W7147022780","doi":"https://doi.org/10.48550/arxiv.2603.28954","title":"Near-Optimal Encodings of Cardinality Constraints","display_name":"Near-Optimal Encodings of Cardinality Constraints","publication_year":2026,"publication_date":"2026-03-30","ids":{"openalex":"https://openalex.org/W7147022780","doi":"https://doi.org/10.48550/arxiv.2603.28954"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.28954","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28954","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.28954","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114881405","display_name":"Andrew Krapivin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Krapivin, Andrew","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009136134","display_name":"Benjamin Przybocki","orcid":"https://orcid.org/0009-0007-5489-1733"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Przybocki, Benjamin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030108071","display_name":"Bernardo Subercaseaux","orcid":"https://orcid.org/0000-0003-2295-1299"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Subercaseaux, Bernardo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.5976999998092651,"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":0.5976999998092651,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.28790000081062317,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.03009999915957451,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.6672000288963318},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.6079000234603882},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5976999998092651},{"id":"https://openalex.org/keywords/hash-function","display_name":"Hash function","score":0.5169000029563904},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.4880000054836273},{"id":"https://openalex.org/keywords/conjunctive-normal-form","display_name":"Conjunctive normal form","score":0.4514999985694885},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.3831000030040741}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6672000288963318},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.6079000234603882},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5976999998092651},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5716000199317932},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.5169000029563904},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.4880000054836273},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.4514999985694885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42899999022483826},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4198000133037567},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3831000030040741},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3386000096797943},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.33059999346733093},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3303000032901764},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32839998602867126},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.2768000066280365},{"id":"https://openalex.org/C9429942","wikidata":"https://www.wikidata.org/wiki/Q1781698","display_name":"Product term","level":5,"score":0.2678999900817871},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.28954","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28954","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.28954","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28954","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,124],"present":[1,29],"several":[2],"novel":[3],"encodings":[4,14,130,146,173],"for":[5,23,33,62,92,112,180,188],"cardinality":[6],"constraints,":[7],"which":[8,104],"use":[9],"fewer":[10],"clauses":[11,151,162],"than":[12],"previous":[13],"and,":[15],"more":[16],"importantly,":[17],"introduce":[18,135],"new":[19],"generally":[20],"applicable":[21],"techniques":[22],"constructing":[24],"compact":[25],"encodings.":[26],"First,":[27],"we":[28,87,134],"a":[30,58,68,76,117,138],"CNF":[31],"encoding":[32,91],"the":[34,47,63,84,106,170],"$\\text{AtMostOne}(x_1,\\dots,x_n)$":[35],"constraint":[36,94,114],"using":[37,147],"$2n":[38,98,148],"+":[39,42,99,149,160,178],"2":[40],"\\sqrt{2n}":[41],"O(\\sqrt[3]{n})$":[43],"clauses,":[44,103],"thus":[45],"refuting":[46],"conjectured":[48],"optimality":[49],"of":[50,71,119,131,175],"Chen's":[51],"product":[52],"encoding.":[53],"Our":[54],"construction":[55,70],"also":[56],"yields":[57],"smaller":[59],"monotone":[60],"circuit":[61,81],"threshold-2":[64],"function,":[65],"improving":[66],"on":[67],"50-year-old":[69],"Adleman":[72],"and":[73,115,122,158,184],"incidentally":[74],"solving":[75],"long-standing":[77],"open":[78],"problem":[79],"in":[80],"complexity.":[82],"On":[83],"other":[85],"hand,":[86],"show":[88],"that":[89],"any":[90],"this":[93,113],"requires":[95],"at":[96],"least":[97],"\\sqrt{n+1}":[100],"-":[101,186],"2$":[102],"is":[105],"first":[107],"nontrivial":[108],"unconditional":[109],"lower":[110],"bound":[111],"answers":[116],"question":[118],"Ku\u010dera,":[120],"Savick\u00fd,":[121],"Vorel.":[123],"then":[125],"turn":[126],"our":[127],"attention":[128],"to":[129,144],"$\\text{AtMost}_k(x_1,\\dots,x_n)$,":[132],"where":[133],"\"grid":[136],"compression\",":[137],"technique":[139],"inspired":[140],"by":[141],"hash":[142],"tables,":[143],"give":[145],"o(n)$":[150,161,179,187],"as":[152,154,163,165],"long":[153,164],"$k":[155,166,181,189],"=":[156,167],"o(\\sqrt[3]{n})$":[157],"$4n":[159],"o(n)$.":[168],"Previously,":[169],"smallest":[171],"known":[172],"were":[174],"size":[176],"$(k+1)n":[177],"\\le":[182],"5$":[183],"$7n":[185],"\\ge":[190],"6$.":[191]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-02T00:00:00"}