{"id":"https://openalex.org/W2602820822","doi":"https://doi.org/10.1145/3039243","title":"Representative Families of Product Families","display_name":"Representative Families of Product Families","publication_year":2017,"publication_date":"2017-03-13","ids":{"openalex":"https://openalex.org/W2602820822","doi":"https://doi.org/10.1145/3039243","mag":"2602820822"},"language":"en","primary_location":{"id":"doi:10.1145/3039243","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3039243","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","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/A5075328697","display_name":"Fedor V. Fomin","orcid":"https://orcid.org/0000-0003-1955-4612"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Fedor V. Fomin","raw_affiliation_strings":["University of Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038531405","display_name":"Daniel Lokshtanov","orcid":"https://orcid.org/0000-0002-3166-9212"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Daniel Lokshtanov","raw_affiliation_strings":["University of Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060986039","display_name":"Fahad Panolan","orcid":"https://orcid.org/0000-0001-6213-8687"},"institutions":[{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Fahad Panolan","raw_affiliation_strings":["The Institute of Mathematical Sciences, HBNI, Chennai, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute of Mathematical Sciences, HBNI, Chennai, India","institution_ids":["https://openalex.org/I59611059"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015806060","display_name":"Saket Saurabh","orcid":"https://orcid.org/0000-0001-7847-6402"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]},{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN","NO"],"is_corresponding":false,"raw_author_name":"Saket Saurabh","raw_affiliation_strings":["The Institute of Mathematical Sciences, HBNI, Chennai, India and University of Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute of Mathematical Sciences, HBNI, Chennai, India and University of Bergen, Norway","institution_ids":["https://openalex.org/I59611059","https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.4784,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.98158746,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"13","issue":"3","first_page":"1","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9973999857902527,"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":0.9932000041007996,"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/family-of-sets","display_name":"Family of sets","score":0.7919822931289673},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7284135818481445},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6563363075256348},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5926946997642517},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.5574785470962524},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4906114637851715},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4446585178375244},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.4421231746673584},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.4305307865142822},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.38831445574760437},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37223508954048157},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20493870973587036}],"concepts":[{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.7919822931289673},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7284135818481445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6563363075256348},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5926946997642517},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.5574785470962524},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4906114637851715},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4446585178375244},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.4421231746673584},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.4305307865142822},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.38831445574760437},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37223508954048157},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20493870973587036},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3039243","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3039243","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W143512583","https://openalex.org/W1565709240","https://openalex.org/W1575411448","https://openalex.org/W1586904125","https://openalex.org/W1816837704","https://openalex.org/W1852383912","https://openalex.org/W1972514464","https://openalex.org/W2008045977","https://openalex.org/W2013902279","https://openalex.org/W2038073775","https://openalex.org/W2059273723","https://openalex.org/W2089369802","https://openalex.org/W2093626764","https://openalex.org/W2094090625","https://openalex.org/W2100239335","https://openalex.org/W2106097003","https://openalex.org/W2162107775","https://openalex.org/W2216833188","https://openalex.org/W2290889164","https://openalex.org/W2296148711","https://openalex.org/W2573633671","https://openalex.org/W2763029945","https://openalex.org/W2793135015","https://openalex.org/W2914414140","https://openalex.org/W2963227734","https://openalex.org/W2990134648","https://openalex.org/W3104156214","https://openalex.org/W3139078859","https://openalex.org/W3209532520","https://openalex.org/W4212992501","https://openalex.org/W4213368513"],"related_works":["https://openalex.org/W2058299944","https://openalex.org/W4323360720","https://openalex.org/W1550144461","https://openalex.org/W4233892543","https://openalex.org/W2783959783","https://openalex.org/W2602164040","https://openalex.org/W2037206237","https://openalex.org/W4310658774","https://openalex.org/W3000635646","https://openalex.org/W2118289204"],"abstract_inverted_index":{"A":[0,18,28,100,111,119,124,126,132,147,178,239],"subfamily":[1],"F\u2032":[2,39,75,158,249],"of":[3,23,58,60,76,78,91,159,165,177,200,257,300,310],"a":[4,35,54,71,104,154,220,272,297],"set":[5,36],"family":[6,56,74,101,106,157,248],"F":[7,14,20,57,77,98,102,116,160,172,207,237,251],"is":[8,103,142,168,271,296],"said":[9],"to":[10,224],"q":[11,25,67,72,92,151,155,183,201,214,246,263],"-":[12],"represent":[13],"if":[15,107],"for":[16,53,95,174,197,204,261,266,280,305],"every":[17],"\u2208":[19,38,125,129],"and":[21,112,150,182,240,242],"B":[22,30,44,113,122,128,130,135,149,180,241],"size":[24,61,79],"such":[26,40,114],"that":[27,41,115,184],"\u2229":[29,43],"=":[31,45,117,136],"\u2205":[32],"there":[33,108],"exists":[34],"A\u2032":[37,42],"\u2205.":[46],"Recently,":[47],"we":[48,86],"provided":[49],"an":[50,65,143,195],"algorithm":[51,144,167,196,227,279],"that,":[52,145],"given":[55,146],"sets":[59],"p":[62],"together":[63],"with":[64],"integer":[66],",":[68,120,127,131,133,148,152,179,181],"efficiently":[69],"computes":[70,153,236,244],"-representative":[73,93,156,202,247,264],"approximately":[80],"(p+q":[81],"p).":[82],"In":[83],"this":[84],"article,":[85],"consider":[87],"the":[88,198,209,230,245,281],"efficient":[89],"computation":[90,199],"families":[94,97,110,203,206,265],"product":[96,105,205,267],".":[99,161,252],"exist":[109],"{":[118],"\u222a,":[121],":":[123],"\u2229,":[134],"\u2205}.":[137],"Our":[138],"main":[139],"technical":[140],"contribution":[141],"The":[162,269,294],"running":[163],"time":[164],"our":[166,258],"sublinear":[169],"in":[170,187,208,219,222],"|":[171,173],"many":[175],"choices":[176],"occur":[185],"naturally":[186],"several":[188],"dynamic":[189,302],"programming":[190,303],"algorithms.":[191],"We":[192,253],"also":[193,216],"give":[194,254],"more":[210],"general":[211],"setting":[212],"where":[213,233],"-representation":[215],"involves":[217],"independence":[218],"matroid":[221],"addition":[223],"disjointness.":[225],"This":[226],"considerably":[228],"outperforms":[229],"naive":[231],"approach":[232],"one":[234],"first":[235,270],"from":[238,250],"then":[243],"two":[255],"applications":[256],"new":[259],"algorithms":[260,304],"computing":[262],"families.":[268],"3.8408":[273],"k":[274,289],"n":[275],"O":[276],"(1)":[277],"deterministic":[278,301],"M":[282,284],"ultilinear":[283],"onomial":[285],"D":[286],"etection":[287],"(":[288],"-M":[290],"l":[291],"D)":[292],"problem.":[293],"second":[295],"significant":[298],"improvement":[299],"\u201cconnectivity":[306],"problems\u201d":[307],"on":[308],"graphs":[309],"bounded":[311],"treewidth.":[312]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":33}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
