{"id":"https://openalex.org/W2031069820","doi":"https://doi.org/10.1145/1127716.1127767","title":"On the complexity of sign-nonsingularity and equal unions of sets","display_name":"On the complexity of sign-nonsingularity and equal unions of sets","publication_year":2000,"publication_date":"2000-04-07","ids":{"openalex":"https://openalex.org/W2031069820","doi":"https://doi.org/10.1145/1127716.1127767","mag":"2031069820"},"language":"en","primary_location":{"id":"doi:10.1145/1127716.1127767","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1127716.1127767","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 38th annual on Southeast regional conference","raw_type":"proceedings-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/A5010007087","display_name":"David P. Jacobs","orcid":"https://orcid.org/0000-0001-9409-0761"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David P. Jacobs","raw_affiliation_strings":["Clemson University, Clemson, SC"],"affiliations":[{"raw_affiliation_string":"Clemson University, Clemson, SC","institution_ids":["https://openalex.org/I8078737"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008224159","display_name":"Robert E. Jamison","orcid":"https://orcid.org/0000-0001-6116-7662"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert E. Jamison","raw_affiliation_strings":["Clemson University, Clemson, SC"],"affiliations":[{"raw_affiliation_string":"Clemson University, Clemson, SC","institution_ids":["https://openalex.org/I8078737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048169846","display_name":"Alice A. McRae","orcid":null},"institutions":[{"id":"https://openalex.org/I430192","display_name":"Appalachian State University","ror":"https://ror.org/051m4vc48","country_code":"US","type":"education","lineage":["https://openalex.org/I430192"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alice A. McRae","raw_affiliation_strings":["Appalachian State Univ., Boone, NC","Appalachian State University, Boone, NC"],"affiliations":[{"raw_affiliation_string":"Appalachian State Univ., Boone, NC","institution_ids":["https://openalex.org/I430192"]},{"raw_affiliation_string":"Appalachian State University, Boone, NC","institution_ids":["https://openalex.org/I430192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010007087"],"corresponding_institution_ids":["https://openalex.org/I8078737"],"apc_list":null,"apc_paid":null,"fwci":0.4542,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65527709,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"232","last_page":"234"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9965999722480774,"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/disjoint-sets","display_name":"Disjoint sets","score":0.7888513207435608},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7726621627807617},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6747345924377441},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6490472555160522},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.6131675243377686},{"id":"https://openalex.org/keywords/disjoint-union","display_name":"Disjoint union (topology)","score":0.563330352306366},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.5565193891525269},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5248872637748718},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4866262376308441},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4371778666973114},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16238951683044434},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10305631160736084},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06751424074172974}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7888513207435608},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7726621627807617},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6747345924377441},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6490472555160522},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.6131675243377686},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.563330352306366},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.5565193891525269},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5248872637748718},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4866262376308441},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4371778666973114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16238951683044434},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10305631160736084},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06751424074172974},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1127716.1127767","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1127716.1127767","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 38th annual on Southeast regional conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1525605957","https://openalex.org/W2011039300","https://openalex.org/W2033401742","https://openalex.org/W2044330456","https://openalex.org/W2064153357","https://openalex.org/W2066561381","https://openalex.org/W2082841621","https://openalex.org/W2085916283","https://openalex.org/W2147282740","https://openalex.org/W2148009509","https://openalex.org/W2158258117","https://openalex.org/W2576233014","https://openalex.org/W4205437167"],"related_works":["https://openalex.org/W2499670206","https://openalex.org/W55187247","https://openalex.org/W2058834578","https://openalex.org/W2091414606","https://openalex.org/W1891636518","https://openalex.org/W2350306728","https://openalex.org/W264408731","https://openalex.org/W2073363580","https://openalex.org/W411819533","https://openalex.org/W2213612705"],"abstract_inverted_index":{"A":[0,43,75],"family":[1,32,44],"of":[2,96,101],"nonempty":[3,18],"sets":[4,47,97],"has":[5,51],"the":[6,22,31,37,52,57,69,102,123],"equal":[7,39,53],"union":[8,40,54],"property":[9,41],"(EUP)":[10],"if":[11,14,60],"and":[12,71,78,85],"only":[13],"there":[15,61],"exist":[16],"two":[17],"disjoint":[19],"subfamilies":[20],"having":[21],"same":[23,94],"union.":[24],"If,":[25],"in":[26,30,122],"addition,":[27],"every":[28],"set":[29],"is":[33,73,104,120],"used,":[34],"we":[35,110],"have":[36],"full":[38],"(FEUP).":[42],"with":[45],"more":[46,63],"than":[48,65],"points":[49,64],"always":[50],"property.":[55],"On":[56],"other":[58],"hand,":[59],"are":[62],"sets,":[66],"recognizing":[67],"both":[68],"EUP":[70,103],"FEUP":[72,119],"NP-complete.":[74],"recent":[76],"striking":[77],"difficult":[79],"result":[80],"by":[81],"Robertson,":[82],"Seymour,":[83],"Thomas,":[84],"independently,":[86],"McCuaig,":[87],"implies":[88],"that":[89,118],"for":[90],"square":[91,124],"families":[92],"(the":[93],"number":[95],"as":[98],"points)":[99],"recognition":[100],"polynomial-time.":[105],"In":[106],"contrast":[107],"to":[108,116],"this,":[109],"give":[111],"a":[112],"simple":[113],"argument":[114],"below":[115],"show":[117],"NP-complete":[121],"case.":[125]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
